The main difference between psi(x;y) and psi(x) in 2D BO is that psi(x;y) is a two-dimensional wavefunction, while psi(x) is a one-dimensional wavefunction. This means that psi(x;y) takes into account both the x and y coordinates, while psi(x) only considers the x coordinate.
Psi(x;y) is represented by a two-dimensional equation, while psi(x) is represented by a one-dimensional equation. This is because psi(x;y) takes into account two variables (x and y), while psi(x) only considers one variable (x).
Psi(x;y) is typically used in situations where the system being studied is two-dimensional, such as in the case of a 2D box potential. This allows for a more accurate representation of the wavefunction and the system as a whole.
The use of psi(x;y) in 2D BO allows for a more detailed understanding of the system being studied. This includes a better understanding of the energy levels, wavefunctions, and other properties of the system. It also allows for a more accurate prediction of experimental results.
No, psi(x;y) and psi(x) cannot be used interchangeably in 2D BO. They represent different mathematical concepts and have different applications in the study of 2D systems. It is important to use the correct wavefunction depending on the system being studied.