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How how can we calculate the future evolution of a particle after the infinite square well potential is (somehow) turned off, releasing it into a free state? Assuming that it was in the ground state before.
Swamp Thing said:Apart from brute force / numerical, is there a nice way to solve this (or to get useful qualitative properties of the solution)? For example, in the absence of ##V(x)##, can we transform the ##\psi(x,t=0)## into ##\psi_p(p,t=0)## and find the future ##\psi_p## in a simple way?
Turning off a square well refers to the sudden removal of a potential barrier that restricts the movement of particles within a confined space. This allows the particles to freely move and interact with each other.
After turning off a square well, the particles within the system will exhibit different behaviors depending on their initial states and interactions. The particles will undergo a process of equilibration, where they reach a state of thermal and energetic balance.
The time evolution of a system after turning off a square well is affected by various factors such as the initial state of the particles, the strength of the interactions between them, and the temperature of the system. The size and shape of the square well also play a role in the time evolution of the system.
The time evolution of a system after turning off a square well can be predicted using mathematical models and simulations. However, the behavior of the system can become unpredictable if the interactions between particles are complex or if there are a large number of particles involved.
The study of time evolution after turning off a square well is relevant in various fields of science, such as physics and chemistry. It helps researchers understand the behavior of particles in different systems and how they reach a state of equilibrium. This knowledge can be applied in designing new materials and understanding the dynamics of complex systems.