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 [tex]\varphi_1(x) [/tex] and [tex] \varphi_2(x)[/tex], with energy eigenvalues [tex] E_1[/tex] and [tex] E_2[/tex].

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

[tex]\phi[/tex]= [tex]c_1*\varphi_1+c_2*\varphi_2[/tex] and [tex] c_1[/tex] and [tex]c_2[/tex]

a) The wave functions [tex] \phi(x,t)[/tex] , 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, [tex] <x>=(\phi,x\phi) [/tex] , as a function , for the state [tex]\phi(x,t)[/tex] from part b.

Homework Equations

The Attempt at a Solution

for part a, should i take the derivative of [tex]\phi[/tex] 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