Unified Description of Matrix Mechanics and Wave Mechanics II

TL;DR

This paper simplifies quantum mechanics by removing bra-ket notation, unifying matrix and wave mechanics through direct matrix representations of operators and wave functions, and providing differential equations for solutions.

Contribution

It introduces a notation-free approach that unifies matrix and wave mechanics, simplifying the fundamental concepts of quantum theory.

Findings

Unified descriptions of matrix and wave mechanics.

Expressed operators, wave functions, and matrices in a single form.

Derived differential equations for solving quantum systems.

Abstract

In this article, we discard the bra-ket notation and its correlative definitions, given by Paul Dirac. The quantum states are only described by the wave functions. The fundamental concepts and definitions in quantum mechanics is simplified. The operator, wave functions and square matrix are represented in the same expression which directly corresponds to the system of equations without additional introduction of the matrix representation of operator. It can make us to convert the operator relations into the matrix relations. According to the relations between the matrices, the matrix elements will be determined. Furthermore, the first order differential equations will be given to find the solution of equations. As a result, we unified the descriptions of the matrix mechanics and the wave mechanics.