Question

Write brief but complete answers to the following questions

a) Write Schrodinger's time-independent,1-D equation

b) What does this equation represent?

c) What requirements must the wave equation satisfy?

d) What are the conditions for an acceptable solution to this equation?

Answer 1

a))

1 D means equation is only is in x or y or z parameter

after simplification we can write it as below

b) this equation represents the wave function of a particle whose energy levels  and position we can determine by this equation , its like equation of motion of a particle in Quantum mechanics

which contains all information to describe a particle  

by the use of this equation tunneling , etc can be explained

The associated wavefunction gives the probability of finding the particle at a certain position.

C & D)  

requirements must the wave equation satisfy

it must satisfy all boundary conditions  

boundary conditions are :

1) wave function must be finite

2)  wave function must be continuous and differentiable everywhere

3) The wave function must be single valued

4)All first-order derivatives of the wave function must be continuous

5 )The wave function must be square-integrable.

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