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Show that [x, p;] = iħ.

Show that [x, p;] = iħ.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 70EQ
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3.1 State the boundary conditions for obtaining the eigenfunctions of a hydrogen atom in terms of u(r). h2 1 d h?1(1+1) 3.2 The radial equation for Hydrogen is given by + V(*)| R(r) = ER(r). 2m r? dr 2mr? Use R(r) = ! to transform it into +V(r)) u(r) = Eu(r). 2m dr2 2mr2 h?1(1+1) 3.3 The effective potential in a Hydrogen atom can be given by Veff(r) = + V(r). Sketch a 2mr? graph which shows the behavior of this effective potential when l 0,1,2. 3.4 Show that [x, pz] = ih.
Transcribed Image Text:3.1 State the boundary conditions for obtaining the eigenfunctions of a hydrogen atom in terms of u(r). h2 1 d h?1(1+1) 3.2 The radial equation for Hydrogen is given by + V(*)| R(r) = ER(r). 2m r? dr 2mr? Use R(r) = ! to transform it into +V(r)) u(r) = Eu(r). 2m dr2 2mr2 h?1(1+1) 3.3 The effective potential in a Hydrogen atom can be given by Veff(r) = + V(r). Sketch a 2mr? graph which shows the behavior of this effective potential when l 0,1,2. 3.4 Show that [x, pz] = ih.
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