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1. (1) Derive one dimensional time-independent Schrödinger equation from the classical wave equation and P=h/n and (2) deduce momentum operator and kinetic energy operator for the wave function y.

1. (1) Derive one dimensional time-independent Schrödinger equation from the classical wave equation and P=h/n and (2) deduce momentum operator and kinetic energy operator for the wave function y.

College Physics
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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1. (1) Derive one dimensional time-independent Schrödinger equation from the classical wave equation and P=h/h and (2) deduce momentum operator and kinetic energy operator for the wave function y. 2. Calculate the specific density function of a single particle, |v|2, on one-dimensional axis (x-axis) including the boundary condition as below; = 00 at x <0 V = 0 at 0 <xSL V = 00 at x>L 3. If the single particle of problem 2 is electron and the L is 10 Å, what are its momentum and energy of the electron with the quantum number of 2? And if there are 1 mole of electrons with the same environment, describe what is the total energy. (mass of electron =9.1 × 10 31 kg, Planck's constant, h= 6.63 × 10-3ª m² kg / s, and Avogadro's number is 6.02 x 10²*. You can choose any unit to show the answer.) 4. Dervie three dimensional time-independent Schrödinger equation for one-electron based on spherical coordinate from Cartesian coordinate system as below. Hemiltonian operator for one-electron system: -h? ( a2 H = 8n2m ax2 ay2 ™ əz? a2 Ze? dy? ' 4πεον2+ y2 + 2?
Transcribed Image Text:1. (1) Derive one dimensional time-independent Schrödinger equation from the classical wave equation and P=h/h and (2) deduce momentum operator and kinetic energy operator for the wave function y. 2. Calculate the specific density function of a single particle, |v|2, on one-dimensional axis (x-axis) including the boundary condition as below; = 00 at x <0 V = 0 at 0 <xSL V = 00 at x>L 3. If the single particle of problem 2 is electron and the L is 10 Å, what are its momentum and energy of the electron with the quantum number of 2? And if there are 1 mole of electrons with the same environment, describe what is the total energy. (mass of electron =9.1 × 10 31 kg, Planck's constant, h= 6.63 × 10-3ª m² kg / s, and Avogadro's number is 6.02 x 10²*. You can choose any unit to show the answer.) 4. Dervie three dimensional time-independent Schrödinger equation for one-electron based on spherical coordinate from Cartesian coordinate system as below. Hemiltonian operator for one-electron system: -h? ( a2 H = 8n2m ax2 ay2 ™ əz? a2 Ze? dy? ' 4πεον2+ y2 + 2?
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