A Particle of Mass m in Infinite 1D State

[Cybercole]

Please help. My professor thinks I know this ****.


Ψ(x,t)=Ae^-a(mx^2/η+it)

A particle of mass m is in the infinite, one-dimensional, time-dependent state:

where A and a are positive real constants. What are: (a) normalization constant A, (b) the potential energy function, U(x), which satisfies Schrödinger equation with (x,t) being its eigenfunction, (c) the quantum-mechanical expectation value of x, (d) the quantum-mechanical expectation value of x2, (e) the quantum-mechanical expectation value of momentum ^p, and (f) the quantum-mechanical expectation value ^p2

 

[dextercioby]

What are your thoughts on this ? Start with point a).

 

[Cybercole]

I honestly don't know where to start. this is the question the teacher gave me.
Can you please help?

 

[dextercioby]

Well, you can't be absolutely clueless. Pick up your theory notes/book. What does normalization constant mean and how do you find it ? Your attitude's not right. You got to show some willingness, else help is not coming to you.

 

[Cybercole]

I know how to normalize a funtion but i am getting stuck in the middle of it... we have never normalize somthing like this before all we have ever done was matrices, i am not very strong in this type of math