# Particle of mass m in a one-dimensional impenetrable box

A particle of mass m is in a one-dimensional impenetrable box extending from x = 0 to x = a. At t = 0, its wavefunction is given as:

(SEE ATTACHMENT FOR EQUATION)

a) What is the probability for finding the particle in the ground state at t = 0?

b) What is the probability of finding the particle between x = 0 to x = al2 at t = 0?

c) Calculate (a) and (b) for time t.

https://brainmass.com/physics/wavefunction/particle-mass-one-dimensional-impenetrable-box-144553

#### Solution Preview

The probability to find the system in state n is the integral of the square of the product of the wave function of the system and the wave function of state n (it's nicer in a formula).

Rewrite the system wavefunction as a linear combination of the particle in a box eigenfunctions, and ...

#### Solution Summary

A particle of mass m is in a one-dimensional impenetrable box extending from x = 0 to x = a. At t = 0, its wavefunction is given as