WebTo get the probabilities of different momenta, you need to Fourier transform the standing wave – a few waves of the sine. One has. ∫ 0 1 d x sin ( n π x) exp ( i p x) = n π [ − 1 + e i p ( − 1) n] p 2 − n 2 π 2. Square the absolute value to get the probability density that the momentum is p. The momentum p should have the natural ... WebJun 13, 2024 · In the case of Particle in a box, V ( x) = 0, for a particle inside the box. And hence, the Schrodinger equation becomes, d 2 ψ d x 2 + k 2 ψ ( x) = 0 where, k = 2 m E ℏ 2 Now, the general solution to such differential equation is given by, ψ ( x) = C 1 e i k x + C 2 e − i k x This can be further be written into,
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