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 2.5, Problem 2.27P
(a)
To determine
To sketch the given double delta potential.
(b)
To determine
The number of bound states, the allowed energies for
(c)
To determine
The bound state energies for the limiting cases (i)
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Problem 2.
Consider the double delta-function potential
V(x) = a[8(x + a) + 8(x − a)],
where a and a are positive constants.
(a) Sketch this potential.
(b) How many bound states does it possess? Find the allowed energies, for a =
ħ²/ma and for a = ħ²/4ma, and sketch the wave functions.
A quantum mechanical particle is confined to a one-dimensional infinite potential well
described by the function V(x) = 0 in the region 0 < x < L, V(x) = ∞ elsewhere.
The normalised eigenfunctions for a particle moving in this potential are:
Yn(x)
=
√
2
Nπ
sin -X
L L
where n = 1, 2, 3, ..
a) Write down the expression for the corresponding probability density function. Sketch
the shape of this function for a particle in the ground state (n = 1).
b) Annotate your sketch to show the probability density function for a classical particle
moving at constant speed in the well. Give a short justification for the shape of your
sketch.
c) Briefly describe, with the aid of a sketch or otherwise, the way in which the quantum
and the classical probability density functions are consistent with the correspondence
principle for large values of n.
Let's consider the two-qubit state
3
|) = 100)+101) +110).
a) Find the expectation values for the values of both qubits separately.
b) The product of qubit values is represented by the operator b₁b2 = (ô× 1) (I Øô) = (ô ❀ô), where
bn is the observable for the value of qubit n. Find the expectation value for the product. For
statistically independent quantities the expectation value of their product is the product of their
expectation values. Are the values of the qubits correlated in state |V)?
c) Show that the state cannot be expressed as a product state, i.e., it is an entangled state.
Chapter 2 Solutions
Introduction To Quantum Mechanics
Ch. 2.1 - Prob. 2.1PCh. 2.1 - Prob. 2.2PCh. 2.2 - Prob. 2.3PCh. 2.2 - Prob. 2.4PCh. 2.2 - Prob. 2.5PCh. 2.2 - Prob. 2.6PCh. 2.2 - Prob. 2.7PCh. 2.2 - Prob. 2.8PCh. 2.2 - Prob. 2.9PCh. 2.3 - Prob. 2.10P
Ch. 2.3 - Prob. 2.11PCh. 2.3 - Prob. 2.12PCh. 2.3 - Prob. 2.13PCh. 2.3 - Prob. 2.14PCh. 2.3 - Prob. 2.15PCh. 2.3 - Prob. 2.16PCh. 2.4 - Prob. 2.17PCh. 2.4 - Prob. 2.18PCh. 2.4 - Prob. 2.19PCh. 2.4 - Prob. 2.20PCh. 2.4 - Prob. 2.21PCh. 2.5 - Prob. 2.22PCh. 2.5 - Prob. 2.23PCh. 2.5 - Prob. 2.24PCh. 2.5 - Prob. 2.25PCh. 2.5 - Prob. 2.26PCh. 2.5 - Prob. 2.27PCh. 2.5 - Prob. 2.28PCh. 2.6 - Prob. 2.29PCh. 2.6 - Prob. 2.30PCh. 2.6 - Prob. 2.31PCh. 2.6 - Prob. 2.32PCh. 2.6 - Prob. 2.34PCh. 2.6 - Prob. 2.35PCh. 2 - Prob. 2.36PCh. 2 - Prob. 2.37PCh. 2 - Prob. 2.38PCh. 2 - Prob. 2.39PCh. 2 - Prob. 2.40PCh. 2 - Prob. 2.41PCh. 2 - Prob. 2.42PCh. 2 - Prob. 2.44PCh. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - Prob. 2.47PCh. 2 - Prob. 2.49PCh. 2 - Prob. 2.50PCh. 2 - Prob. 2.51PCh. 2 - Prob. 2.52PCh. 2 - Prob. 2.53PCh. 2 - Prob. 2.54PCh. 2 - Prob. 2.58PCh. 2 - Prob. 2.63PCh. 2 - Prob. 2.64P
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