Due to the wall, there is no translation symmetry and momentum is not a good quantum number. However, momentum squared is. Combining eigenfunctions of positive and negative momentum you can get eigenfunctions of the Hamiltonian that satisfy the appropriate boundary condition.Christopher Grayce said:
Particle motion in a rigid box refers to the movement of a particle within a confined, non-flexible container. This type of motion is often studied in physics and can be used to understand the behavior of gases, liquids, and other substances.
The motion of a particle in a rigid box can be solved using mathematical equations and principles, such as Newton's laws of motion and the ideal gas law. These equations can be used to calculate the position, velocity, and acceleration of the particle at any given time.
The value of t=0 represents the initial time or starting point in the motion of the particle. It is used as a reference point for calculating the particle's position, velocity, and acceleration at any other time during its motion.
Yes, there are some assumptions made when solving particle motion in a rigid box. These include assuming that the box is completely rigid and does not change shape, and that there are no external forces acting on the particle besides those specified in the problem.
Solving particle motion in a rigid box can be applied in many real-life situations, such as understanding the behavior of gases in a container, predicting the trajectory of a projectile, or simulating the movement of molecules in a chemical reaction. It can also be used to design and optimize various mechanical systems, such as engines and turbines.
