General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Question
Chapter 28, Problem 48E
To determine
The probability to find the particle within the given range.
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This is a textbook question, not a graded question
The wave function for a quantum particle confined to moving in a one-dimensional box located between x = 0 and x = L is ψ(x) = A sin (nπx/L)Use the normalization condition on ψ to show that A = √2/L
Chapter 28 Solutions
General Physics, 2nd Edition
Ch. 28 - Prob. 1RQCh. 28 - Prob. 2RQCh. 28 - Prob. 3RQCh. 28 - Prob. 4RQCh. 28 - Prob. 5RQCh. 28 - Prob. 6RQCh. 28 - Prob. 7RQCh. 28 - Prob. 8RQCh. 28 - Prob. 9RQCh. 28 - Prob. 10RQ
Ch. 28 - Prob. 1ECh. 28 - Prob. 2ECh. 28 - Prob. 3ECh. 28 - Prob. 4ECh. 28 - Prob. 5ECh. 28 - Prob. 6ECh. 28 - Prob. 7ECh. 28 - Prob. 8ECh. 28 - Prob. 9ECh. 28 - Prob. 10ECh. 28 - Prob. 11ECh. 28 - Prob. 12ECh. 28 - Prob. 13ECh. 28 - Prob. 14ECh. 28 - Prob. 15ECh. 28 - Prob. 16ECh. 28 - Prob. 17ECh. 28 - Prob. 18ECh. 28 - Prob. 19ECh. 28 - Prob. 20ECh. 28 - Prob. 21ECh. 28 - Prob. 22ECh. 28 - Prob. 23ECh. 28 - Prob. 24ECh. 28 - Prob. 25ECh. 28 - Prob. 26ECh. 28 - Prob. 27ECh. 28 - Prob. 28ECh. 28 - Prob. 29ECh. 28 - Prob. 30ECh. 28 - Prob. 31ECh. 28 - Prob. 32ECh. 28 - Prob. 33ECh. 28 - Prob. 34ECh. 28 - Prob. 35ECh. 28 - Prob. 36ECh. 28 - Prob. 37ECh. 28 - Prob. 38ECh. 28 - Prob. 39ECh. 28 - Prob. 40ECh. 28 - Prob. 41ECh. 28 - Prob. 42ECh. 28 - Prob. 43ECh. 28 - Prob. 44ECh. 28 - Prob. 45ECh. 28 - Prob. 46ECh. 28 - Prob. 47ECh. 28 - Prob. 48ECh. 28 - Prob. 49ECh. 28 - Prob. 50ECh. 28 - Prob. 51ECh. 28 - Prob. 52ECh. 28 - Prob. 53ECh. 28 - Prob. 54E
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- Show that the two lowest energy states of the simple harmonic oscillator, 0(x) and 1(x) from Equation 7.57, satisfy Equation 7.55. n(x)=Nne2x2/2Hn(x),n=0,1,2,3,.... h2md2(x)dx2+12m2x2(x)=E(x).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_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
- If the ground state energy of a simple harmonic oscillator is 1.25 eV, what is the frequency of its motion?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_forwardIf in a box with infinite walls of size 1 nm there is an electron in the energy state n=2, find its probability density, the wave function and the corresponding energy.arrow_forward
- Prove that assuming n = 0 for a quantum particle in an infinitely deep potential well leads to a violation of the uncertainty principle Δpx Δx ≥ h/2.arrow_forwardWhat is the probability of finding a particle in the last 10% of a one-dimensional box for n = 1 state? Find the solution(s) to the differential equations: a. y''(x) + y'(x) - 6y(x) = 0 and b. y''(x) - 4y'(x) + 4y(x) = 0.arrow_forwardFor 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.arrow_forward
- An electron is trapped in a one-dimensional infinite potential well in a state with quantum number n = 17. How many points of (a) zero probability and (b) maximum probability does its matter wave have?arrow_forwardA Quantum system has a ground state with energy E0 = 100meV and a 3-fold degenerate excited state with energy E1 = 100meV . Calculate the probability of finding the system in its groud state when it is at T = 300 K? a) 0.94 b) 0.06 c) 1 d) 0.98arrow_forward
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