A Modern Approach to Quantum Mechanics · Problem 6.20

The One-Dimensional Harmonic Oscillator — John S. Townsend

Physics — Quantum Mechanics · momentum-probability-delta-function-eigenstate

Problem

Normalize the wave function

\langle x|\psi\rangle = \begin{cases} Ne^{-\kappa x} & x > 0 \\ Ne^{\kappa x} & x < 0 \end{cases}

Determine the probability that a measurement of the momentum

p

finds the momentum between

p

and

p + dp

for this wave function. Note: This wave function is the energy eigenfunction for the delta function potential energy well of Problem 6.19.