What is a Wave function in quantum physics?
Answer:- A wave function is a mathematical description of a quantum state of a particle as a function of momentum, time, position and spin. The symbol used for a wave function is a Greek letter called psi, ψ. It helps us to know the probability of finding particle within the matter.
Characteristics of wave function:-
- Contains all measurable information about the particle.
- ψ should be continuous and single-valued.
- ψ should be finite.
- ψ should be square Integrable.
- ψ2 gives us probability of finding the particle.
Boundary Conditions:-
- In order to avoid infinite probabilities, ψ must be finite everywhere.
- In order to avoid multiple values of the probability, ψ must be single valued.
- For finite potentials, the wave function and its derivative must be continuous. This is required because the second order derivative term in the wave equation must be single valued.
- In order to normalize the wave function, it must approach zero as x approaches infinity.
Particle in a Three Dimensional Box :-
The quantum particle in the 1D box problem can be expanded to consider a particle within higher
dimensions.
Consider a particle which can move freely with in a box of dimensions
