onsider the radial momentum operator, p, = -ih(0/ar + 1/r), then e radial part of the Hamiltonian is written as h? 1 a 2m r2 dr' ar 2m

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
1
Calculate (1/r*) in the eigenstates of hydrogen in the following way:
Consider the radial momentum operator, pr =-
ih(a/ar + 1/r), then
the radial part of the Hamiltonian is written as
h? 1 a
2m r2 Or' dr
2m
Use ([H, p,]) = 0 in the energy eigenstates, and by explicitly evaluating
commutator to show that
(4)-win (4)
1
%3D
p3
1(1 + 1)ao \r2
Transcribed Image Text:Calculate (1/r*) in the eigenstates of hydrogen in the following way: Consider the radial momentum operator, pr =- ih(a/ar + 1/r), then the radial part of the Hamiltonian is written as h? 1 a 2m r2 Or' dr 2m Use ([H, p,]) = 0 in the energy eigenstates, and by explicitly evaluating commutator to show that (4)-win (4) 1 %3D p3 1(1 + 1)ao \r2
Expert Solution
steps

Step by step

Solved in 3 steps

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,