Question

which condition id sufficient to ensure that a wave function is an energy eigenfunction?

a. the wave function is normalizable

b. the wave function satosfoes the time independent schrodinger equation

Answer #1

A wave function to be an energy eigenfunction must satisfy the time independent Schrödinger equation.

This is the difference between an eigenfunction and a wave function. If an operator operated on a wave function gives the same wave function then that wave function will be an eigenfunction.That's why all eigen functions are wavefunctions but not the vice versa.

Schrödinger's equation consists of two operators- potential and kinetic energy operator.So an eigenfunction will satisfy it.

And the result obtained will be an energy eigen value..

If u face any problem, plz comment...

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