Eigenfunctions and Particle Position Expectation in One Dimension

[noblegas]

Homework Statement

Consider a particle that moves in one dimension. Two of its normalized energy eigenfunctions are \varphi_1(x) and \varphi_2(x), with energy eigenvalues E_1 and E_2.

At time t=0 the wave function for the particle is

\phi= c_1*\varphi_1+c_2*\varphi_2 and c_1 and c_2

a) The wave functions \phi(x,t) , as a function of time , in terms of the given constants and initials condition.

b) Find and reduce to the simplest possible form, an expression for the expectation value of the particle position, <x>=(\phi,x\phi) , as a function , for the state \phi(x,t) from part b.

Homework Equations

The Attempt at a Solution

for part a, should i take the derivative of \phi with respect to t?

 

[Matterwave]

For part a you need to use the Schroedinger's equation to know how the state evolves as a function of time, but you need to know the potential the particle is in...does the problem specify a potential?

 

[noblegas]

No , they don't specify the value of the potential