Show that the time-dependent Schrödinger equation preserves the normalizationof the wavefunction, i.e.If a function y(x,t) is normalized at t=0, i.e.[y*(x,0)y/(x,0)dx = 1ootootand y(x,t) satisfies the time-dependent Schrodinger equation, i.e.дф(x, t)ħ² d²(x, t)ihƏt2m dx²then y(x,t) is normalized at any later moment in time t, i.e.fy*(x,t)y(x,t)dx=1_ for any t.-00-∞0+ V (x, t)(x, t)Note: it is possible to prove this even for an arbitrary time-dependent potential energyV(x, t). Thus the wavefunction that satisfies the time-dependent Schrodinger equationautomatically obeys the normalization condition.Hint: Calculate the time derivative of the normalization integral and prove that it is zero.

Here, if ψ(x,t) is normalized at t=0,…

Show that the time-dependent Schrödinger equation preserves the normalization of the wavefunction, i.e. If a function y(x, t) is normalized at t=0, i.e. +∞o [y*(x,0)y/(x,0)dx = 1 -8 and y(x,t) satisfies the time-dependent Schrodinger equation, i.e. дф(x, t) ħ² d²(x, t) ih Ət 2m dx² then y(x,t) is normalized at any later moment in time t, i.e. +∞o [y*(x,t)y(x,t)dx=1_for any t. -00 + V (x, t)(x, t) Note: it is possible to prove this even for an arbitrary time-dependent potential energy V(x,t). Thus the wavefunction that satisfies the time-dependent Schrodinger equation automatically obeys the normalization condition. Hint: Calculate the time derivative of the normalization integral and prove that it is zero.

Show that the time-dependent Schrödinger equation preserves the normalization of the wavefunction, i.e. If a function y(x, t) is normalized at t=0, i.e. +∞o [y(x,0)y/(x,0)dx = 1 -8 and y(x,t) satisfies the time-dependent Schrodinger equation, i.e. дф(x, t) ħ² d²(x, t) ih Ət 2m dx² then y(x,t) is normalized at any later moment in time t, i.e. +∞o [y(x,t)y(x,t)dx=1_for any t. -00 + V (x, t)(x, t) Note: it is possible to prove this even for an arbitrary time-dependent potential energy V(x,t). Thus the wavefunction that satisfies the time-dependent Schrodinger equation automatically obeys the normalization condition. Hint: Calculate the time derivative of the normalization integral and prove that it is zero.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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