Newbie's Fundamental Doubt: Wave Function & Eigen Functions

[Shalini]

Hi...I am new to this forum.
Can somebody clear a fundamental doubt i have? A wave function has a form found by applying Schrödinger's equation. In steady-state systems, arent the system eigen functions, the wave equation of the system? if so is it the energy eigen function or the momentum eigen function(say in particle in a box problem) or eigen function of some other observable that is its wave function?

 

[mjsd]

you should clear up your question first. I've found it hard to follow and not sure what you are actually asking.

in short a wave fn represents the state of the system. it is a collection of variables that describe that state.

 

[StatusX]

Stationary states are typically states that are eigenstates of the energy operator. They are called stationary because their time dependence of the simple form:

$$\Psi(x,t) = \psi(x) e^{i E t/\hbar}$$

Since wavefunctions are really only determined up to an arbitrary phase anyway, this means the state doesn't change in time.

In the same way that an eigenstate of energy is constant (up to a phase) in time, an eigenstate of momentum is constant (up to a phase) in position. In particular, no state in the particle in a box system is an eignestate of momentum.