CRC Press eBooks

Dirac's Notation Identities

F.J. Duarte

Published Jan 15, 2024• 0 citations

Abstract

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.

DOI: 10.1201/9781003398707-6

Related papers

Quantum Entanglement Probability Amplitude for n = N = 21, 22, 23,…, 2 r

F.J. Duarte

The generalized probability amplitude, or state, for quantum entanglement, for n = N = 2 1 , 2 2 , 2 3 , … 2 r is derived in a clear and transparent approach from the Dirac–Feynman N -slit superposition probability amplitude. In other words, from probability amplitudes in quantum interference to the generalized probability amplitudes in quantum entanglement, via the | X 〉 = | a 〉 1 , | b 〉 2 , | c 〉 3 …| g 〉 n Dirac identity.

CRC Press eBooksJan 15, 20240 citations

Quantum Entanglement Probability Amplitudes for n = N = 3, 6

F.J. Duarte

The generalized probability amplitude, or state, for quantum entanglement, for n = N = 3, 6, is derived in a clear and transparent approach from the Dirac–Feynman N -slit superposition probability amplitude. In other words, from probability amplitudes in quantum interference to probability amplitudes in quantum entanglement, via the | X 〉= | a 〉 1 , | b 〉 2 , | c 〉 3 …| g 〉 n Dirac identity, and quaternions.

CRC Press eBooksJan 15, 20240 citations

Quantum Entanglement Probability Amplitude for n = N = 2

F.J. Duarte

The probability amplitude, or state, for quantum entanglement in its most basic form, a photon pair and two channels of propagation ( n = N = 2), is derived in a clear and transparent approach from the Dirac–Feynman N -slit superposition probability amplitude. In other words, from probability amplitudes in quantum interference to probability amplitudes in quantum entanglement, via the | X 〉 = | a 〉 1 , | b 〉 2 , | c 〉 3 …| g 〉 n Dirac identity.

CRC Press eBooksJan 15, 20240 citations

Probability Amplitudes

F. J. Duarte

Quantum mechanics runs on probability amplitudes. Probability amplitudes must accurately describe the physics prior to calculating the quantum probability. Symbolical probability amplitudes are mathematically represented by complex wave functions. Many physicists in the field don’t even mention the words probability amplitude and prefer to refer to wave function, or state, instead. When they do that they miss out on the subtleties of the physics at hand. In this brief chapter we emphasize probability amplitudes à la Dirac since that is the way Feynman and Ward preferred to describe quantum mechanics. The Dirac notation is also ideally suited to describe quantum interference and quantum entanglement.

CRC Press eBooksApr 10, 20260 citations

Dirac Notation Identities

F.J. Duarte

As described by Dirac (1978) and Feynman et al. (1965) , the Dirac notation includes various mathematical properties and allows for various abstractions and permutations. Here, a few useful set of identities and properties of the notation are described.

CRC Press eBooksOct 29, 20130 citations

Dirac Quantum Optics

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.

CRC Press eBooksOct 29, 20130 citations