Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Question
Chapter 9.3, Problem 9.6P
(a)
To determine
The potential energy above the floor in terms of
(b)
To determine
To solve the Schrodinger equation having potential
(c)
To determine
The first four allowed energies in joules.
(d)
To determine
The ground state energy of electron in
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The following problem arises in quantum mechanics (see Chapter 13, Problem 7.21). Find the number of ordered triples of nonnegative integers a, b, c whose sum a+b+c is a given positive integer n. (For example, if n = 2, we could have (a, b, c) = (2, 0, 0) or (0, 2, 0) or (0, 0, 2) or (0, 1, 1) or (1, 0, 1) or (1, 1, 0).) Hint: Show that this is the same as the number of distinguishable distributions of n identical balls in 3 boxes, and follow the method of the diagram in Example 5.
Consider the half oscillator" in which a particle of mass m is restricted to the region x > 0 by the potential energy
U(x) = 00
for a O
where k is the spring constant.
What are the energies of the ground state and fırst excited state? Explain your reasoning.
Give the energies in terms of the oscillator frequency wo =
Vk/m.
Formulas.pdf (Click here-->)
Consider the three-dimensional harmonic oscillator, for which the potential is
V ( r ) = 1/2 m ω2 r2
(a) Show that the separation of variables in Cartesian coordinates turns this into three one-dimensional oscillators, and exploit your knowledge of the latter to determine the allowed energies.
Answer: En = ( n + 3/2 ) ħ ω
(b) Determine the degeneracy d ( n ) of En
Chapter 9 Solutions
Introduction To Quantum Mechanics
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