Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 33B / a / i

Table of contents
- Solution i

Solution

Since

O

commutes with every angular momentum operator, it commutes with

J^{2}

. Taking a matrix element of

[O, J^{2}] = 0

gives

(j^{'} (j^{'} + 1) - j (j + 1)) ⟨ j, m ∣ O ∣ j^{'}, m^{'} ⟩ = 0.

The allowed nonnegative values of

j

make

j (j + 1)

injective, so the matrix element vanishes unless

j = j^{'}

.

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version