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jimmycricket
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If you are given the state of a system at t=0 in vector form, how do you find the wave function for arbitrary t?
A time dependent wave function is a mathematical function used to describe the behavior of a quantum system over time. It is a solution to the Schrödinger equation and contains information about the probability of finding a particle at a specific position and time.
The time dependent wave function takes into account the change in the quantum system over time, while the time independent wave function does not. The time dependent wave function includes a time variable, while the time independent wave function does not.
The time dependent wave function can be affected by external forces, such as electric or magnetic fields, as well as the potential energy of the system. It can also be affected by the initial conditions of the system.
The time dependent wave function is a fundamental concept in quantum mechanics and is used to calculate the probability of a particle's position and momentum at any given time. It is also used to study the behavior of quantum systems and make predictions about their future states.
The time dependent wave function is typically represented by the Greek letter psi (ψ) and is a function of both position and time. It can be written as ψ(x,t), where x represents position and t represents time. It is a complex-valued function and can be visualized as a wave in the position-time plane.