- #1
Philip Land
- 56
- 3
Hi!
When calculating ##(\hat{a} \hat{a}^{\dagger})^2## i get ##\hat{a} \hat{a} \hat{a}^{\dagger} \hat{a}^{\dagger}## which is perfectly fine.
But how do I end up with the ultimate simplified expression $$\hat{ a}^{\dagger} \hat{a} \hat{a}^{\dagger} \hat{a} + \hat{a}^{\dagger} \hat_{a} + 2\hat{a}^{\dagger} \hat_{a} + 2 = N^2 + 3 N +1 $$
Are there any definitions, rules or framework I can use to carry out these calculations to make my life easier or do I simply need to write out the definitions of ## \hat{a}^{\dagger}## and ##\hat{a}## and tediously recognize each term?
When calculating ##(\hat{a} \hat{a}^{\dagger})^2## i get ##\hat{a} \hat{a} \hat{a}^{\dagger} \hat{a}^{\dagger}## which is perfectly fine.
But how do I end up with the ultimate simplified expression $$\hat{ a}^{\dagger} \hat{a} \hat{a}^{\dagger} \hat{a} + \hat{a}^{\dagger} \hat_{a} + 2\hat{a}^{\dagger} \hat_{a} + 2 = N^2 + 3 N +1 $$
Are there any definitions, rules or framework I can use to carry out these calculations to make my life easier or do I simply need to write out the definitions of ## \hat{a}^{\dagger}## and ##\hat{a}## and tediously recognize each term?