Introduction to Quantum Mechanics · Problem 2.7

Time-Independent Schrödinger Equation — David J. Griffiths

Physics — Quantum Mechanics · infinite_square_well

Problem

A particle in the infinite square well has the initial wave function Ψ(x,0)={Ax,0≤x≤a/2,A(a−x),a/2≤x≤a.\Psi(x, 0) = \begin{cases} Ax, & 0 \le x \le a/2, \\ A(a - x), & a/2 \le x \le a. \end{cases} (a) Sketch Ψ(x,0)\Psi(x, 0), and determine the constant AA. (b) Find Ψ(x,t)\Psi(x, t). (c) What is the probability that a measurement of the energy would yield the value E1E_1? (d) Find the expectation value of the energy, using Equation 2.21.

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