PC4201 QUANTUM MECHANICS
PC4201 QUANTUM MECHANICS
Tutorial 3 (Angular Momentum)
1. Show that if the (2k + 1) operators [pic] satisfy the commutation relations
[pic] , [pic] [pic].
the (2k + 1) operators [pic] have the same property.
2. We denote by [pic] the following function of the operator A and the components of angular momentum: [pic][pic].
Show that if [pic] is a k th-order irreducible tensor operator, its components verify the relation
[pic]
3. Let [pic] be the annihilation and creation operators of a two-dimensional, isotropic, harmonic oscillator: [pic]
We write
[pic]
[pic]
[pic]
J1, J2, J3 may be considered as the Cartesian coordinates of a certain vector operator [pic].
Show that the components of [pic]verify the commutation relations [pic]characteristic of an angular momentum, and that one has
[pic]
(therefore [pic]) .
OCH/RW/ 99/00
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- sungard quantum treasury management system
- sungard quantum treasury workstation
- iop quantum 2020
- quantum harmonic oscillators
- quantum harmonic oscillator solution
- quantum mechanical harmonic oscillator
- quantum harmonic oscillator 2d
- quantum mechanics chemistry problems
- quantum physics problems and solutions
- quantum harmonic oscillator pdf
- quantum physicist education requirements
- quantum harmonic oscillator wikipedia