A particle in the infinite well of width from Chapter 5 is prepared in the superposition

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · The formalism of quantum mechanics · The formalism of quantum mechanics

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Observables, commutators and the uncertainty relations

Problem

A particle in the infinite well of width

a

from Chapter 5 is prepared in the superposition

\Psi(x,0) = \dfrac{1}{\sqrt5}\psi_1(x) + \dfrac{2}{\sqrt5}\psi_2(x)

, where

\psi_n

and

E_n = n^2\pi^2\hbar^2/2ma^2

are the well's eigenfunctions and energies. Find the probability of each possible outcome of an energy measurement, and

\langle H\rangle

in units of

E_1