Is this homework?Joydeep Munshi said:Hi,
in case of a particle inside a box (infinite square well), can degeneracy occur for different energy eigen states?
please explain...
A "particle in a box" is a simplified theoretical model used in quantum mechanics to explain the behavior of a particle confined to a one-dimensional space. It assumes that the particle is completely free to move inside the box, but cannot leave its boundaries.
Degeneracy refers to the fact that multiple states of a particle in a box can have the same energy level. This means that there can be more than one possible configuration of the particle with the same energy, leading to degenerate energy levels.
Degeneracy is important because it affects the possible energy levels and configurations of a particle in a box. It also plays a crucial role in explaining phenomena such as the heat capacity of solids and the electronic structure of atoms and molecules.
The equation for calculating the degeneracy of a particle in a box is given by: degeneracy = nx * ny * nz, where nx, ny, and nz represent the number of energy levels in the x, y, and z directions, respectively.
The degeneracy of a particle in a box increases as the box size increases. This is because a larger box allows for more possible energy states and therefore, more degeneracy. On the other hand, as the box size decreases, the degeneracy decreases as there are fewer possible energy levels for the particle to occupy.