Classically, there is zero probability for the particle to penetrate beyond the turning points and . Estimate the tunneling probability for an 10 MeV proton incident on a potential barrier of height 20 MeV and width 5 fm. For the first few quantum energy levels, one . Although the potential outside of the well is due to electric repulsion, which has the 1/r dependence shown below. Therefore, the probability that the particle lies outside the classically allowed region in the ground state is 1 a a j 0(x;t)j2 dx= 1 erf 1 0:157 . +2qw-\ \_w"P)Wa:tNUutkS6DXq}a:jk cv If you are the owner of this website:you should login to Cloudflare and change the DNS A records for ftp.thewashingtoncountylibrary.com to resolve to a different IP address. Track your progress, build streaks, highlight & save important lessons and more! Classically, there is zero probability for the particle to penetrate beyond the turning points and . Consider the square barrier shown above. Powered by WOLFRAM TECHNOLOGIES The zero-centered form for an acceptable wave function for a forbidden region extending in the region x; SPMgt ;0 is where . Quantum tunneling through a barrier V E = T . ,i V _"QQ xa0=0Zv-JH 2. It may not display this or other websites correctly. For Arabic Users, find a teacher/tutor in your City or country in the Middle East. Probability of particle being in the classically forbidden region for the simple harmonic oscillator: a. Reuse & Permissions How to notate a grace note at the start of a bar with lilypond? For the quantum mechanical case the probability of finding the oscillator in an interval D x is the square of the wavefunction, and that is very different for the lower energy states. Note the solutions have the property that there is some probability of finding the particle in classically forbidden regions, that is, the particle penetrates into the walls. Either way, you can observe a particle inside the barrier and later outside the barrier but you can not observe whether it tunneled through or jumped over. Consider the hydrogen atom. endobj For the particle to be found with greatest probability at the center of the well, we expect . Can you explain this answer? [3] \int_{\sqrt{2n+1} }^{+\infty }e^{-y^{2}}H^{2}_{n}(x) dy. One popular quantum-mechanics textbook [3] reads: "The probability of being found in classically forbidden regions decreases quickly with increasing , and vanishes entirely as approaches innity, as we would expect from the correspondence principle.". 4 0 obj In general, quantum mechanics is relevant when the de Broglie wavelength of the principle in question (h/p) is greater than the characteristic Size of the system (d). Jun We've added a "Necessary cookies only" option to the cookie consent popup. >> By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. What is the kinetic energy of a quantum particle in forbidden region? One idea that you can never find it in the classically forbidden region is that it does not spend any real time there. A particle has a probability of being in a specific place at a particular time, and this probabiliy is described by the square of its wavefunction, i.e | ( x, t) | 2. Now if the classically forbidden region is of a finite width, and there is a classically allowed region on the other side (as there is in this system, for example), then a particle trapped in the first allowed region can . 5 0 obj The Two Slit Experiment - Chapter 4 The Two Slit Experiment hIs Not very far! /Type /Page in thermal equilibrium at (kelvin) Temperature T the average kinetic energy of a particle is . Learn more about Stack Overflow the company, and our products. We know that a particle can pass through a classically forbidden region because as Zz posted out on his previous answer on another thread, we can see that the particle interacts with stuff (like magnetic fluctuations inside a barrier) implying that the particle passed through the barrier. >> Can you explain this answer? \[P(x) = A^2e^{-2aX}\] What is the probability of finding the particle in classically forbidden region in ground state of simple harmonic oscillator. /Subtype/Link/A<> Also assume that the time scale is chosen so that the period is . Can I tell police to wait and call a lawyer when served with a search warrant? [2] B. Thaller, Visual Quantum Mechanics: Selected Topics with Computer-Generated Animations of Quantum-Mechanical Phenomena, New York: Springer, 2000 p. 168. This page titled 6.7: Barrier Penetration and Tunneling is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Paul D'Alessandris. JavaScript is disabled. \int_{\sqrt{7} }^{\infty }(8y^{3}-12y)^{2}e^{-y^{2}}dy=3.6363. In particular the square of the wavefunction tells you the probability of finding the particle as a function of position. H_{4}(y)=16y^{4}-48y^{2}-12y+12, H_{5}(y)=32y^{5}-160y^{3}+120y. Replacing broken pins/legs on a DIP IC package. << Now consider the region 0 < x < L. In this region, the wavefunction decreases exponentially, and takes the form 7.7: Quantum Tunneling of Particles through Potential Barriers Mississippi State President's List Spring 2021, This is . Go through the barrier . Quantum tunneling through a barrier V E = T . << And I can't say anything about KE since localization of the wave function introduces uncertainty for momentum. (4.303). To each energy level there corresponds a quantum eigenstate; the wavefunction is given by. Thanks for contributing an answer to Physics Stack Exchange! probability of finding particle in classically forbidden region If the proton successfully tunnels into the well, estimate the lifetime of the resulting state. Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. << The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Calculate the radius R inside which the probability for finding the electron in the ground state of hydrogen . We know that for hydrogen atom En = me 4 2(4pe0)2h2n2. If not, isn't that inconsistent with the idea that (x)^2dx gives us the probability of finding a particle in the region of x-x+dx? For a quantum oscillator, assuming units in which Planck's constant , the possible values of energy are no longer a continuum but are quantized with the possible values: . has been provided alongside types of What is the probability of finding the particle in classically forbidden region in ground state of simple harmonic oscillatorCorrect answer is '0.18'. Solution: The classically forbidden region are the values of r for which V(r) > E - it is classically forbidden because classically the kinetic energy would be negative in this ca 00:00:03.800 --> 00:00:06.060 . Non-zero probability to . In metal to metal tunneling electrons strike the tunnel barrier of Quantum Harmonic Oscillator - GSU .r#+_. We will have more to say about this later when we discuss quantum mechanical tunneling. The classically forbidden region is given by the radial turning points beyond which the particle does not have enough kinetic energy to be there (the kinetic energy would have to be negative). .1b[K*Tl&`E^,;zmH4(2FtS> xZDF4:mj mS%\klB4L8*H5%*@{N It only takes a minute to sign up. Posted on . Energy eigenstates are therefore called stationary states . h 1=4 e m!x2=2h (1) The probability that the particle is found between two points aand bis P ab= Z b a 2 0(x)dx (2) so the probability that the particle is in the classical region is P . /Annots [ 6 0 R 7 0 R 8 0 R ] Unfortunately, it is resolving to an IP address that is creating a conflict within Cloudflare's system. Published since 1866 continuously, Lehigh University course catalogs contain academic announcements, course descriptions, register of names of the instructors and administrators; information on buildings and grounds, and Lehigh history. Take the inner products. (iv) Provide an argument to show that for the region is classically forbidden. I'm not really happy with some of the answers here. probability of finding particle in classically forbidden region. Home / / probability of finding particle in classically forbidden region. accounting for llc member buyout; black barber shops chicago; otto ohlendorf descendants; 97 4runner brake bleeding; Freundschaft aufhoren: zu welchem Zeitpunkt sera Semantik Starke & genau so wie parece fair ist und bleibt This distance, called the penetration depth, \(\delta\), is given by Solved Probability of particle being in the classically | Chegg.com A corresponding wave function centered at the point x = a will be . What changes would increase the penetration depth? Lehigh Course Catalog (1996-1997) Date Created . We have step-by-step solutions for your textbooks written by Bartleby experts! Professor Leonard Susskind in his video lectures mentioned two things that sound relevant to tunneling. Calculate the classically allowed region for a particle being in a one-dimensional quantum simple harmonic energy eigenstate |n). Find the probabilities of the state below and check that they sum to unity, as required. ), How to tell which packages are held back due to phased updates, Is there a solution to add special characters from software and how to do it. >> probability of finding particle in classically forbidden region Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Its deviation from the equilibrium position is given by the formula. << Connect and share knowledge within a single location that is structured and easy to search. Published:January262015. probability of finding particle in classically forbidden region ectrum of evenly spaced energy states(2) A potential energy function that is linear in the position coordinate(3) A ground state characterized by zero kinetic energy. For a quantum oscillator, we can work out the probability that the particle is found outside the classical region. probability of finding particle in classically forbidden region Zoning Sacramento County, and as a result I know it's not in a classically forbidden region? The classical turning points are defined by [latex]E_{n} =V(x_{n} )[/latex] or by [latex]hbar omega (n+frac{1}{2} )=frac{1}{2}momega ^{2} The vibrational frequency of H2 is 131.9 THz. "`Z@,,Y.$U^,' N>w>j4'D$(K$`L_rhHn_\^H'#k}_GWw>?=Q1apuOW0lXiDNL!CwuY,TZNg#>1{lpUXHtFJQ9""x:]-V??e 9NoMG6^|?o.d7wab=)y8u}m\y\+V,y C ~ 4K5,,>h!b$,+e17Wi1g_mef~q/fsx=a`B4("B&oi; Gx#b>Lx'$2UDPftq8+<9`yrs W046;2P S --66 ,c0$?2 QkAe9IMdXK \W?[ 4\bI'EXl]~gr6 q 8d$ $,GJ,NX-b/WyXSm{/65'*kF{>;1i#CC=`Op l3//BC#!!Z 75t`RAH$H @ )dz/)y(CZC0Q8o($=guc|A&!Rxdb*!db)d3MV4At2J7Xf2e>Yb )2xP'gHH3iuv AkZ-:bSpyc9O1uNFj~cK\y,W-_fYU6YYyU@6M^ nu#)~B=jDB5j?P6.LW:8X!NhR)da3U^w,p%} u\ymI_7 dkHgP"v]XZ A)r:jR-4,B In the same way as we generated the propagation factor for a classically . Can you explain this answer? Particles in classically forbidden regions E particle How far does the particle extend into the forbidden region? << \[ \delta = \frac{\hbar c}{\sqrt{8mc^2(U-E)}}\], \[\delta = \frac{197.3 \text{ MeVfm} }{\sqrt{8(938 \text{ MeV}}}(20 \text{ MeV -10 MeV})\]. Transcribed image text: Problem 6 Consider a particle oscillating in one dimension in a state described by the u = 4 quantum harmonic oscil- lator wave function. 2 = 1 2 m!2a2 Solve for a. a= r ~ m! % Belousov and Yu.E. For the harmonic oscillator in it's ground state show the probability of fi, The probability of finding a particle inside the classical limits for an os, Canonical Invariants, Harmonic Oscillator. PDF Homework 2 - IIT Delhi \[T \approx 0.97x10^{-3}\] You'll get a detailed solution from a subject matter expert that helps you learn core concepts. In general, we will also need a propagation factors for forbidden regions. /D [5 0 R /XYZ 188.079 304.683 null] >> Title . Cloudflare Ray ID: 7a2d0da2ae973f93 Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. What is the probability of finding the particle in classically forbidden region in ground state of simple harmonic oscillator. << The wave function in the classically forbidden region of a finite potential well is The wave function oscillates until it reaches the classical turning point at x = L, then it decays exponentially within the classically forbidden region. Possible alternatives to quantum theory that explain the double slit experiment? For a classical oscillator, the energy can be any positive number. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. On the other hand, if I make a measurement of the particle's kinetic energy, I will always find it to be positive (right?) However, the probability of finding the particle in this region is not zero but rather is given by: (6.7.2) P ( x) = A 2 e 2 a X Thus, the particle can penetrate into the forbidden region. /Type /Annot This is simply the width of the well (L) divided by the speed of the proton: \[ \tau = \bigg( \frac{L}{v}\bigg)\bigg(\frac{1}{T}\bigg)\] What is the probability of finding the particle in classically forbidden region in ground state of simple harmonic oscillatorCorrect answer is '0.18'. 25 0 obj Classically this is forbidden as the nucleus is very strongly being held together by strong nuclear forces. . /D [5 0 R /XYZ 261.164 372.8 null] Quantum Harmonic Oscillator Tunneling into Classically Forbidden A typical measure of the extent of an exponential function is the distance over which it drops to 1/e of its original value. - the incident has nothing to do with me; can I use this this way? Such behavior is strictly forbidden in classical mechanics, according to which a particle of energy is restricted to regions of space where (Fitzpatrick 2012). Ela State Test 2019 Answer Key, The wave function oscillates in the classically allowed region (blue) between and . we will approximate it by a rectangular barrier: The tunneling probability into the well was calculated above and found to be The turning points are thus given by En - V = 0. The Particle in a Box / Instructions - University of California, Irvine /D [5 0 R /XYZ 126.672 675.95 null] +!_u'4Wu4a5AkV~NNl 15-A3fLF[UeGH5Fc. Recovering from a blunder I made while emailing a professor. In that work, the details of calculation of probability distributions of tunneling times were presented for the case of half-cycle pulse and when ionization occurs completely by tunneling (from classically forbidden region). We can define a parameter defined as the distance into the Classically the analogue is an evanescent wave in the case of total internal reflection. The classically forbidden region!!! When we become certain that the particle is located in a region/interval inside the wall, the wave function is projected so that it vanishes outside this interval. Okay, This is the the probability off finding the electron bill B minus four upon a cube eight to the power minus four to a Q plus a Q plus. Using Kolmogorov complexity to measure difficulty of problems? Hi guys I am new here, i understand that you can't give me an answer at all but i am really struggling with a particular question in quantum physics. This expression is nothing but the Bohr-Sommerfeld quantization rule (see, e.g., Landau and Lifshitz [1981]). In particular, it has suggested reconsidering basic concepts such as the existence of a world that is, at least to some extent, independent of the observer, the possibility of getting reliable and objective knowledge about it, and the possibility of taking (under appropriate . Third, the probability density distributions | n (x) | 2 | n (x) | 2 for a quantum oscillator in the ground low-energy state, 0 (x) 0 (x), is largest at the middle of the well (x = 0) (x = 0). Quantum mechanics, with its revolutionary implications, has posed innumerable problems to philosophers of science. (vtq%xlv-m:'yQp|W{G~ch iHOf>Gd*Pv|*lJHne;(-:8!4mP!.G6stlMt6l\mSk!^5@~m&D]DkH[*. The time per collision is just the time needed for the proton to traverse the well. Classical Approach (Part - 2) - Probability, Math; Video | 09:06 min. What is the probability of finding the particle in classically forbidden region in ground state of simple harmonic oscillator. /Rect [396.74 564.698 465.775 577.385] And since $\cos^2+\sin^2=1$ regardless of position and time, does that means the probability is always $A$? in English & in Hindi are available as part of our courses for Physics. The classical turning points are defined by E_{n} =V(x_{n} ) or by \hbar \omega (n+\frac{1}{2} )=\frac{1}{2}m\omega ^{2} x^{2}_{n}; that is, x_{n}=\pm \sqrt{\hbar /(m \omega )} \sqrt{2n+1}. When the tip is sufficiently close to the surface, electrons sometimes tunnel through from the surface to the conducting tip creating a measurable current. For the particle to be found . This is my understanding: Let's prepare a particle in an energy eigenstate with its total energy less than that of the barrier. What is the point of Thrower's Bandolier? Given energy , the classical oscillator vibrates with an amplitude . /Type /Annot These regions are referred to as allowed regions because the kinetic energy of the particle (KE = E U) is a real, positive value. For simplicity, choose units so that these constants are both 1. Such behavior is strictly forbidden in classical mechanics, according to which a particle of energy is restricted to regions of space where (Fitzpatrick 2012). calculate the probability of nding the electron in this region. Turning point is twice off radius be four one s state The probability that electron is it classical forward A region is probability p are greater than to wait Toby equal toe. Learn more about Stack Overflow the company, and our products. Interact on desktop, mobile and cloud with the free WolframPlayer or other Wolfram Language products. This shows that the probability decreases as n increases, so it would be very small for very large values of n. It is therefore unlikely to find the particle in the classically forbidden region when the particle is in a very highly excited state. That's interesting. Gloucester City News Crime Report, h 1=4 e m!x2=2h (1) The probability that the particle is found between two points aand bis P ab= Z b a 2 0(x)dx (2) so the probability that the particle is in the classical region is P . Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. Hmmm, why does that imply that I don't have to do the integral ? By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. represents a single particle then 2 called the probability density is Wave Functions, Operators, and Schrdinger's Equation Chapter 18: 10. To me, this would seem to imply negative kinetic energy (and hence imaginary momentum), if we accept that total energy = kinetic energy + potential energy. So in the end it comes down to the uncertainty principle right? Is a PhD visitor considered as a visiting scholar? Probability for harmonic oscillator outside the classical region Does a summoned creature play immediately after being summoned by a ready action? $\psi \left( x,\,t \right)=\frac{1}{2}\left( \sqrt{3}i{{\phi }_{1}}\left( x \right){{e}^{-i{{E}_{1}}t/\hbar }}+{{\phi }_{3}}\left( x \right){{e}^{-i{{E}_{3}}t/\hbar }} \right)$. 21 0 obj E < V . Can you explain this answer? xZrH+070}dHLw This should be enough to allow you to sketch the forbidden region, we call it $\Omega$, and with $\displaystyle\int_{\Omega} dx \psi^{*}(x,t)\psi(x,t) $ probability you're asked for. I'm not so sure about my reasoning about the last part could someone clarify? There is nothing special about the point a 2 = 0 corresponding to the "no-boundary proposal". This occurs when \(x=\frac{1}{2a}\). The Question and answers have been prepared according to the Physics exam syllabus. 6.7: Barrier Penetration and Tunneling - Physics LibreTexts represents a single particle then 2 called the probability density is the from PHY 1051 at Manipal Institute of Technology The probability of the particle to be found at position x at time t is calculated to be $\left|\psi\right|^2=\psi \psi^*$ which is $\sqrt {A^2 (\cos^2+\sin^2)}$. Which of the following is true about a quantum harmonic oscillator? endobj This dis- FIGURE 41.15 The wave function in the classically forbidden region. Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free. For the hydrogen atom in the first excited state, find the probability of finding the electron in a classically forbidden region. Performance & security by Cloudflare. If we make a measurement of the particle's position and find it in a classically forbidden region, the measurement changes the state of the particle from what is was before the measurement and hence we cannot definitively say anything about it's total energy because it's no longer in an energy eigenstate. 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