Commutator: Hamiltonian and position

00:15 Introduction 00:34 Hamiltonian and position operators in QM 01:06 Explicit forms of kinetic energy operator T and position operator x 01:30 Use of property of commutator to write commutator as sum of two commutators 02:04 Since position commutes with potential energy function V, second commutator equals 0 02:16 Definition of commutator 02:35 Addition of dummy argument Ψ 02:59 Grouping of operators 03:15 Replacement of "first" (rightmost) operator by explicit form 04:05 Replacement of "second" (leftmost) operator by explicit form 04:40 Pull constants in front of derivatives 05:53 Use fact that the second derivative is the first derivative of the first derivative 06:05 Use product rule to find first derivative 07:22 Differentiate second time 08:01 Combine like terms 08:15 Cancel additive inverses 08:38 Cancel factor of 2 08:52 Use fact that 𝘪 × 𝘪 = -1 09:30 Use explicit form of momentum operator in QM Color-coded, step-by-step calculation of the commutator of the Hamiltonian operator (in one dimension) and position. Don't forget to like, comment, share, and subscribe!