Dirac Notation and Principles of Quantum Mechanics

F.J. Duarte

The Paul Adrien Maurice Dirac notation is one of the mathematical avenues that can be used to describe nature quantum mechanically. This mathematical notation was invented by Dirac in 1939 and is particularly well suited to describe quantum optics. In Principles of Quantum Mechanics, first published in 1930, Dirac discusses the essence of interference as a one-photon phenomenon. Albeit his discussion is qualitative, it is also profound. In 1965, R. P. Feynman discussed electron interference via a two-slit thought experiment using probability amplitudes and the Dirac notation as a tool. The Dirac notation offers a natural avenue to describe the propagation of particles from a source to a detection plane, via a pair of slits. This was done by Feynman in a thought experiment using electrons and two slits.

Yuyu ZHANG, Zi-Xiang Hu, Jianjun Dong +1 more

When teaching quantum mechanics, little consideration is given to the dimensional aspect of wave functions and the Dirac notation. The introduction of the Dirac notation, with its bra and ket vectors, is a powerful tool for describing quantum states. However, the question of whether the Dirac notation has dimensions is rarely discussed. It seems that it is commonly assumed that the Dirac notation is merely a dimensionless mathematical symbol. In this article, we will discuss the dimensional aspect of wave functions and the Dirac notation, which will help students develop a deeper understanding of the meaning behind quantum mechanical symbols.

F.J. Duarte

Dirac’s notation identities are listed in a handbook style. Particular attention is given to | X 〉 = | a 〉 1 , | b 〉 2 , | c 〉 3 … | g 〉 n that plays a central role in the derivation of the probability amplitude for quantum entanglement from quantum interferometric principles.

Manuel Gadella, F. Gómez-Cubillo