Particle In 3 Dimensional Box

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:- 

1. Contains all measurable information about the particle.
2. ψ should be continuous and single-valued.
3. ψ should be finite.
4. ψ should be square Integrable.
5. ψ2 gives us probability of finding the particle.

Boundary Conditions:-

1. In order to avoid infinite probabilities, ψ must be finite everywhere.
2. In order to avoid multiple values of the probability, ψ must be single valued.
3. 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.
4.  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