Comparing Wave Functions: Are \psi_{1} and \psi_{2} in the Same Quantum State?

[Axiom17]

Homework Statement

To determine whether two wave functions, \psi_{1} and \psi_{1} correspond to the same quantum state of a particle.

Homework Equations

Calculations (simplified):

\psi_{1}(x,y,z)=A

\psi_{2}(x,y,z)=e^{z}A

The Attempt at a Solution

The two wave functions do correspond to the same quantum state. However I can't figure out the correct wording to explain this. At the moment I just have that "\psi_{1} is equal to \psi_{2} with respect to the independant variable z in the term e^{z}".

Hopefully that's correct, or at least it makes some sense.. sure there's probably a better (more correct) way to write it though. :shy:

 

[fzero]

Homework Statement

To determine whether two wave functions, \psi_{1} and \psi_{1} correspond to the same quantum state of a particle.

Homework Equations

Calculations (simplified):

\psi_{1}(x,y,z)=A

\psi_{2}(x,y,z)=e^{z}A

The Attempt at a Solution

The two wave functions do correspond to the same quantum state. However I can't figure out the correct wording to explain this. At the moment I just have that "\psi_{1} is equal to \psi_{2} with respect to the independant variable z in the term e^{z}".

Hopefully that's correct, or at least it makes some sense.. sure there's probably a better (more correct) way to write it though. :shy:

You should use the relation of wavefunctions to quantum states. For instance in the coordinate basis |\vec{x}\rangle, we can write

|\psi_1 \rangle = \int d\vec{x}~ \psi_1(\vec{x}) |\vec{x}\rangle .

Then one way to show that two wavefunctions describe the same state would be to show that

\langle \vec{x}|\psi_1 \rangle =\langle\vec{x}|\psi_2 \rangle

 

[arkajad]

Are you sure there is e^z and not e^{iz} in your problem? Just checking ...