Get Critique of Recent Quantum Theories. II PDF

By Seeger R.

Show description

Read or Download Critique of Recent Quantum Theories. II PDF

Similar quantum physics books

Read e-book online Introduction to Quantum Mechanics PDF

While this vintage textual content was once first released in 1935, it fulfilled the objective of its authors "to produce a textbook of useful quantum mechanics for the chemist, the experimental physicist, and the start scholar of theoretical physics. " even though many that are academics this present day as soon as labored with the publication as scholars, the textual content remains to be as beneficial for a similar undergraduate viewers.

Extra resources for Critique of Recent Quantum Theories. II

Sample text

The Bogoliubov transformation in Eq. 42) is linear, since it transforms a mode operator into a linear combination of other mode operators. As we have seen, these linear transformations are induced by generators (Hamiltonians) that are quadratic in the mode operators. In particular, both (generalized) beam splitter and squeezing transformations are generated by quadratic Hamiltonians. On the other hand, when people mention linear optics, they often refer specifically to optical elements that are described by generalized beam splitters, and not squeezers.

214), we can evaluate the expectation values of various important operators. First, the expectation value of the annihilation and creation operators are α, ξ| a ˆ |α, ξ = α and α, ξ| a ˆ† |α, ξ = α∗ . 216) The average photon number in a squeezed coherent state is α, ξ| n ˆ |α, ξ = sinh2 |ξ| + |α|2 . 217) 48 The quantum theory of light The expectation values of the mode operators also immediately allows us to calculate the expectation value of an arbitrary field quadrature operator: 1 α, ξ| x ˆζ |α, ξ = √ α e−iζ + α∗ eiζ ≡ xζ (α) .

In this Section we study how linear and quadratic functions of the mode operators can be used to define two important classes of states of the electromagnetic field. Linear Hamiltonians give rise to coherent states, while quadratic Hamiltonians produce squeezed states. Coherent states We can define states according to the operators that produce them out of the vacuum. For example, as in Eq. 62), the n-photon Fock state in a normalized mode a is produced by the operator n a ˆ† |n = √ |0 . 176) n! 177) 42 The quantum theory of light where the cn are complex amplitudes and n |cn |2 = 1†.

Download PDF sample

Rated 4.26 of 5 – based on 44 votes