![]() ![]() ![]() derivation of error estimates between the original solution. Setting boundary conditions as \(x=0\), \(u(x=0,t) = 0\) and \(x = \ell\), \(u(x=\ell, t) = 0\) allows for this partial differential equation to be solved (to see it in action in the lab see ). Schrdinger equation describes how the quantum state of some physical system changes with time. Let us begin with the physical motivation, reviewing both the classical and quantum mechanics of a simple. Consider a 'free particle state' corresponding to (V0): a. Where \(v\) is the velocity of disturbance along the string. There are actually two (closely related) variants of Schrodinger’s equation, the time dependent Schrodinger equation and the time independent Schrodinger equation we will begin with the discussion of the time-dependent equation. The time-dependent Schrödinger equation is a partial differential equation that describes how the wavefunction evolves over time, while the time-independent Schrödinger equation is an equation of state for wavefunctions of definite energy. ![]()
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