Quantum Mechanics

9

Bra and Ket Vector Formalism and Symmetries

In the previous chapters, quantum mechanics, based on Schrödinger’s differential equations called wave mechanics, was discussed. Here the operators were differential operators like −iħ d/dx for momentum or multiplicative factors like xⁿ. This is not the only formulation of quantum mechanics. There is indeed another formulation of quantum mechanics called matrix mechanics in which all the dynamical variables are represented by matrices. For instance, the operators X_op and P_op are represented by infinite dimensional matrices [x] and [p] such that [x][p]−[p][x] = iħ[1] where [1] is an infinite dimensional unit matrix. In fact, matrix mechanics was developed by Heisenberg and others earlier to Schrödinger’s ...