Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 11.5, Problem 11.19P
To determine
The probability that measurement of energy is
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Students have asked these similar questions
Consider a 1-dimensional quantum system of one particle
Question 01:
in which the particle is under a potential V(x) = mw?a?, with m being the
mass of the particle and w being a parameter (you may take it as angular fre-
quency) with inverse dimension of time. The particle may be found in the region
-0 < x < o.
Varify that the lowest two states of the system are mutually orthonormal.
Let's consider a harmonic oscillator. The total energy of
this oscillator is given by E=(p²/2m) +(½)kx?.
A) For constant energy E, graph the energies in the
range E to E + dE, the allowed region in the classical
phase space (p-x plane) of the oscillator.
B) For k = 6.0 N / m, m = 3.0 kg and the maximum
amplitude of the oscillator xmax =2.3 m For the
region with energies equal to or less than E, the
oscillator number of states that can be entered D(E).
Physics Department
PHYS4101 (Quantum Mechanics)
Assignment 2 (Fall 2020)
Name & ID#.
A three-dimensional harmonic oscillator of mass m has the potential energy
1
1
1
V(x.y.2) = ; mw*x² +mwży² +=mw;z?
where w1 = 2w
a. Write its general eigenvalues and eigenfunctions
b. Determine the eigenvalues and their degeneracies up to the 4th excited state
c. The oscillator is initially equally likely found in the ground, first and second excited states and
is also equally likely found among the states of the degenerate levels. Calculate the expectation
values of the product xyz at time t
Chapter 11 Solutions
Introduction To Quantum Mechanics
Ch. 11.1 - Prob. 11.1PCh. 11.1 - Prob. 11.2PCh. 11.1 - Prob. 11.3PCh. 11.1 - Prob. 11.4PCh. 11.1 - Prob. 11.5PCh. 11.1 - Prob. 11.6PCh. 11.1 - Prob. 11.7PCh. 11.1 - Prob. 11.8PCh. 11.1 - Prob. 11.9PCh. 11.3 - Prob. 11.10P
Ch. 11.3 - Prob. 11.11PCh. 11.3 - Prob. 11.12PCh. 11.3 - Prob. 11.13PCh. 11.3 - Prob. 11.14PCh. 11.3 - Prob. 11.15PCh. 11.3 - Prob. 11.16PCh. 11.4 - Prob. 11.17PCh. 11.5 - Prob. 11.18PCh. 11.5 - Prob. 11.19PCh. 11.5 - Prob. 11.20PCh. 11.5 - Prob. 11.21PCh. 11.5 - Prob. 11.22PCh. 11 - Prob. 11.23PCh. 11 - Prob. 11.24PCh. 11 - Prob. 11.25PCh. 11 - Prob. 11.26PCh. 11 - Prob. 11.27PCh. 11 - Prob. 11.28PCh. 11 - Prob. 11.29PCh. 11 - Prob. 11.30PCh. 11 - Prob. 11.31PCh. 11 - Prob. 11.33PCh. 11 - Prob. 11.35PCh. 11 - Prob. 11.36PCh. 11 - Prob. 11.37P
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