Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 5, Problem 31E
To determine
To Verify:
If
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A function of the form e^−gx2 is a solution of the Schrodinger equation for the harmonic oscillator, provided that g is chosen correctly. In this problem you will find the correct form of g.
(a) Start by substituting Ψ = e^−gx2 into the left-hand side of the Schrodinger equation for the harmonic oscillator and evaluating the second derivative.
(b) You will find that in general the resulting expression is not of the form constant × Ψ, implying that Ψ is not a solution to the equation. However, by choosing the value of g such that the terms in x^2 cancel one another, a solution is obtained. Find the required form of g and hence the corresponding energy.
(c) Confirm that the function so obtained is indeed the ground state of the harmonic oscillator and has the correct energy.
Obtain the schrodinger equation in spherical polar coordinates by using the schrodinger equation given in (x,y,z) Cartesian coordinate system.
The 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?
Chapter 5 Solutions
Modern Physics
Ch. 5 - Prob. 1CQCh. 5 - Prob. 2CQCh. 5 - Prob. 3CQCh. 5 - Prob. 4CQCh. 5 - Prob. 5CQCh. 5 - Prob. 6CQCh. 5 - Prob. 7CQCh. 5 - Prob. 8CQCh. 5 - Prob. 9CQCh. 5 - Prob. 10CQ
Ch. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - Prob. 13CQCh. 5 - Prob. 14CQCh. 5 - Prob. 15CQCh. 5 - Prob. 16CQCh. 5 - Prob. 17CQCh. 5 - Prob. 18CQCh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - Prob. 37ECh. 5 - Prob. 38ECh. 5 - Prob. 39ECh. 5 - Prob. 40ECh. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Obtain expression (5-23) from equation (5-22)....Ch. 5 - Prob. 44ECh. 5 - Prob. 45ECh. 5 - Prob. 46ECh. 5 - Prob. 47ECh. 5 - Prob. 48ECh. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - Prob. 53ECh. 5 - Prob. 54ECh. 5 - Prob. 55ECh. 5 - Prob. 56ECh. 5 - Prob. 57ECh. 5 - Prob. 58ECh. 5 - Prob. 59ECh. 5 - Prob. 60ECh. 5 - Prob. 61ECh. 5 - Prob. 62ECh. 5 - Prob. 63ECh. 5 - Prob. 64ECh. 5 - Prob. 65ECh. 5 - Prob. 66ECh. 5 - Prob. 67ECh. 5 - Prob. 68ECh. 5 - Prob. 69ECh. 5 - Prob. 70ECh. 5 - Prob. 71ECh. 5 - In a study of heat transfer, we find that for a...Ch. 5 - Prob. 73CECh. 5 - Prob. 74CECh. 5 - Prob. 75CECh. 5 - Prob. 76CECh. 5 - Prob. 77CECh. 5 - Prob. 78CECh. 5 - Prob. 79CECh. 5 - Prob. 80CECh. 5 - Prob. 81CECh. 5 - Prob. 82CECh. 5 - Prob. 83CECh. 5 - Prob. 84CECh. 5 - Prob. 85CECh. 5 - Prob. 86CECh. 5 - Prob. 87CECh. 5 - Prob. 88CECh. 5 - Consider the differential equation...Ch. 5 - Prob. 90CECh. 5 - Prob. 91CECh. 5 - Prob. 92CECh. 5 - Prob. 93CECh. 5 - Prob. 94CECh. 5 - Prob. 95CECh. 5 - Prob. 96CECh. 5 - Prob. 97CECh. 5 - Prob. 98CE
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