University Physics Volume 3
17th Edition
ISBN: 9781938168185
Author: William Moebs, Jeff Sanny
Publisher: OpenStax
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Textbook Question
Chapter 7, Problem 84AP
Consider an infinite square well with wall boundaries
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Using the wave function and energy E, apply the Schrodinger equation for the particle within the box.
Solve the Schrodinger equation for a quantum particle of massm trapped in a one-dimensional infinite potential well (box) oflength L and obtain the expressions for wave-functions of theparticle.
For a particle in a 1-dimensional infinitely deep box of length L, the normalized wave function or the 1st excited state can be written as:
Ψ2(x) = {1/i(2L)1/2} ( eibx -e-ibx), where b = 2π/L.
Give the full expression that you need to solve to determine the probalibity of finding the particle in the 1st third of the box. Simplify as much as possible but do not solve any integrals.
Chapter 7 Solutions
University Physics Volume 3
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L] is in the third excited...Ch. 7 - A 0.20-kg billiard ball bounces back and forth...Ch. 7 - Find the expectation value of the position squared...Ch. 7 - Consider an infinite square well with wall...Ch. 7 - Consider an infinite square well with wall...Ch. 7 - Atoms in a crystal lattice vibrate in simple...Ch. 7 - A diatomic molecule behaves like a quantum...Ch. 7 - An electron with kinetic energy 2.0 MeV encounters...Ch. 7 - A beam of mono-energetic protons with energy 2.0...Ch. 7 - An electron in a long, organic molecule used in a...Ch. 7 - In STM, an elevation of the tip above the surface...Ch. 7 - If STM is to detect surface features with local...Ch. 7 - Use Heisenberg's uncertainty principle to estimate...Ch. 7 - Suppose an infinite square well extends from L/2...Ch. 7 - A particle of mass m confined to a box of width L...
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- Consider an infinite square well with wall boundaries x=0 and x=L. Show that the function (x)=Asinkx is the solution to the stationary Schrödinger equation for the particle in a box only if k=2mE/h. Explain why this is an acceptable wave function only if k is an integer multiple of /L.arrow_forwardA particle of mass m confined to a box of width L is in its first excited state 2(x). (a) Find its average position (which is the expectation value of the position). (b) Where is the particle most likely to found?arrow_forwardSuppose a wave function is discontinuous at some point. Can this function represent a quantum state of some physical particle? Why? Why not?arrow_forward
- Find the expectation value x2 of the square of the position for a quantum harmonic oscillator in the ground state. Note: +dxx2ea x 2=(2a 3/2)1.arrow_forwardA particle of mass m is confined to a box of width L. If the particle is in the first excited state, what are the probabilities of finding the particle in a region of width0.020 L around the given point x: (a) x=0.25L; (b) x=040L; (c) 0.75L and (d) x=0.90L.arrow_forwardCan we measure the energy of a free localized particle with complete precision?arrow_forward
- Consider a particle of mass m, located in a potential energy well.one-dimensional (box) with infinite height walls. The wave function that describes this system is:Ψn(x) = K sin (nπx /L), for 0 ≤ x ≤ LΨn(x) = 0 for any other value.K is a constant and n = 1,2,3,... Determine K*K = │K│2arrow_forwardThe normalized solution to the Schrodinger equation for a particular potential is ψ = 0 for x <0, and Ψ(x)=(2/a^{3/2}) x exp(-ax) for x>=0. What is the probability of finding a particle at this potential between x = a - 0.027a and x = a + 0.027a? a) 4,7%b)4,1%c)1,5%d)2,9%e)2,0%arrow_forward
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