Commutations Relations | Quantum Mechanics | Solved Problems
An important role in quantum theory is played by the so-called representations of commutation relations. The question is to determine (up to unitary equivalence) all the solutions of specific operator equations containing commutators (or anti-commutators {T1, T2} = T1T2 + T2T1; we do not discuss this case here). The commutator of operators T1, T2 on H is defined by [T1, T2] = T1T2 − T2T1. We restrict ourselves to the case of a finite number m of degrees of freedom.
We derive an expression for the commutator of functions of operators with constant commutations relations in terms of the partial derivatives of these functions. This result extends the well-known commutation relation between one operator and a function of another operator. We discuss the range of applicability of the formula with examples in quantum mechanics.
For More Information
Watch Video On YouTube
https://youtu.be/0bDEZkxvh1E
#Blogspot
#QuantumMechanics
#Cummutationsrelations
#SolvedProblems
Comments
Post a Comment