![]() ![]() ![]() (7) Which is the famous time dependent Schrodinger wave equation. Now taking results from equation (3) and (5) we can write the equation (6) as, h2 2m 2 x2 + V(x) i t. Essentially a wave equation, the Schrödinger equation describes the form of the probability waves (or wave functions see de Broglie wave) that govern the motion of small particles, and it specifies how these waves are altered by external influences. So, despite both of them being wave solutions, we can see that they are structurally quite different as the structure of a wave-solution is contained in. 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 ). (6) Here, is the wave function of a particle moving in the presence of a potential V(x). In particular, the free-particle solution of the Schrödinger equation has a quadratic dispersion relation while the solution of the classical wave-equation has a linear dispersion relation. Let us begin with the physical motivation, reviewing both the classical and quantum mechanics of a simple. 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. ![]()
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