Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 4.5, Problem 4.44P
To determine

The proof that the wave function given by equation 4.197 satisfies Schrodinger’s equation.

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4.10 A particle is bound in a one-dimensional potential V(x), where V(x) is symmetric, i.e., V(x) = V(−x). = −x, (a) Suppose that (x) is a solution of the Schrödinger equation with energy E. Make the change of variables y and show that (y) is also a solution of the Schrödinger equation with energy E. (b) Since the solutions of the Schrödinger equation for a fixed value of E are unique (up to multiplication by a constant), the result from part (a) implies that √(x) = c(-x), where c is an unknown constant. Use this result to show that (x) must be either even [(x) = (x)] or odd [(-x) = v(x)]. (c) For a particle bound in a one-dimensional symmetric potential, so that V(x) = V (x), show that all of the following are true: (i) * is a symmetric function, (ii) (x) = 0, (iii) (p) = 0.
I have an electron that I want to put in a rigid box. How small do I need to make the box so that the speed of my electron in its ground state inside the box will be equal to the speed of light? Include a sketch of U(x) and ?(x). Sketch the situation, defining all your variables.
Consider the function v(1,2) =( [1s(1) 3s(2) + 3s(1) 1s(2)] [x(1) B(2) + B(1) a(2)] Which of the following statements is incorrect concerning p(1,2) ? a. W(1,2) is normalized. Ob. The function W(1,2) is symmetric with respect to the exchange of the space and the spin coordinates of the two electrons. OC. y(1,2) is an eigenfunction of the reference (or zero-order) Hamiltonian (in which the electron-electron repulsion term is ignored) of Li with eigenvalue = -5 hartree. d. The function y(1,2) is an acceptable wave function to describe the properties of one of the excited states of Lit. Oe. The function 4(1,2) is an eigenfunction of the operator S,(1,2) = S;(1) + S,(2) with eigenvalue zero.
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