What is the Exponential Function in Quantum Mechanics?

[whitegirlandrew]

Homework Statement

The question is here.
http://postimg.org/image/l7aw07sr9/

Homework Equations

The Attempt at a Solution

I don't even understand what it's asking because how can a stationary state be an exponential function with no boundaries? I would appreciate any insight, thank you.

 

[nrqed]

Homework Statement

The question is here.
http://postimg.org/image/l7aw07sr9/

Homework Equations

The Attempt at a Solution

I don't even understand what it's asking because how can a stationary state be an exponential function with no boundaries? I would appreciate any insight, thank you.

I am not sure what you mean by "no boundaries". The wave function must be zero at x=0 and it must go to zero sufficiently fast at x = infinity, and what is provided fulfills those two conditions.

The first step is to determine if this is a state of definite energy (an eigenstate of the hamiltonian). It is, the eigenvalue will give the energy. Do you see how to check if it's an eigenstate?

 

[whitegirlandrew]

I am not sure what you mean by "no boundaries". The wave function must be zero at x=0 and it must go to zero sufficiently fast at x = infinity, and what is provided fulfills those two conditions.

The first step is to determine if this is a state of definite energy (an eigenstate of the hamiltonian). It is, the eigenvalue will give the energy. Do you see how to check if it's an eigenstate?

We did not go over those concepts.

 

[nrqed]

We did not go over those concepts.

Have you learned about Schrodinger's equation or the hamiltonian?

 

[whitegirlandrew]

Have you learned about Schrodinger's equation or the hamiltonian?

We learned about schrodinger's equation. It's a second year course so it doesn't deal with the pure mathematics of solving the equation but we went through on how it was 'derived', and various solutions such as the infinite and finite potential well.

 

[nrqed]

We learned about schrodinger's equation. It's a second year course so it doesn't deal with the pure mathematics of solving the equation but we went through on how it was 'derived', and various solutions such as the infinite and finite potential well.

Ok, good. Then all you have to do is to plug the wave function they give into Schrodinger's equation (using for V(x) the potential they give) and then isolate E. That will give you the energy of that state.

 

[whitegirlandrew]

Ok, good. Then all you have to do is to plug the wave function they give into Schrodinger's equation (using for V(x) the potential they give) and then isolate E. That will give you the energy of that state.

Then what about the integral given below? What does that have to do with anything.

 

[nrqed]

Then what about the integral given below? What does that have to do with anything.

The integral will be needed to determine the constant "A", you will need to impose that the integral of $|\psi|^2 dx$ from 0 to infinity gives 1 and that will fix the value of A. Note that in the first step, when you plug in the wave function in the equation, the A will cancel out everywhere so in that step you will not fix the value of A.

I must correct one thing: when you plug in the wave function in Schrodinger's equation, you will also be able to determine the value of "b" that appears in the exponential, so at that stage you will be able to determine both E and b.

 

[whitegirlandrew]

The integral will be needed to determine the constant "A", you will need to impose that the integral of $|\psi|^2 dx$ from 0 to infinity gives 1 and that will fix the value of A. Note that in the first step, when you plug in the wave function in the equation, the A will cancel out everywhere so in that step you will not fix the value of A.

I must correct one thing: when you plug in the wave function in Schrodinger's equation, you will also be able to determine the value of "b" that appears in the exponential, so at that stage you will be able to determine both E and b.

I Think i somewhat understand, I will give it a try, thank you for the help.

 

[nrqed]

I Think i somewhat understand, I will give it a try, thank you for the help.

You are very welcome. If you get stuck, post here what you tried.