Partition functions and symmetric polynomials
We find a close correspondence between the partition functions of ideal quantum gases and certain symmetric polynomials. From this correspondence, it can be shown that a number of thermodynamic identi...
We find a close correspondence between the partition functions of ideal quantum gases and certain symmetric polynomials. From this correspondence, it can be shown that a number of thermodynamic identi...
The attractive nonlinear delta-function potential
We solve the one-dimensional nonlinear Schrödinger equation for an attractive delta-function potential at the origin, [(p2/2m)–(x)|(x)|](x) = E(x), and obtain the bound state in closed form ...
We solve the one-dimensional nonlinear Schrödinger equation for an attractive delta-function potential at the origin, [(p2/2m)–(x)|(x)|](x) = E(x), and obtain the bound state in closed form ...
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The calculated photon: Visualization of a quantum field
American Journal of Physics -- January 2002 -- Volume 70, Issue 1, pp. 58-66
Issue Date: January 2002
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We calculate spatial localization and phase properties of spontaneously emitted photons. Our model is simple yet fully quantized: the emitting atom is a two-level atom located in a one-dimensional multimode optical cavity. Although the photon state vector does not have a position-space representation, the expectation value of the square of the electric field operator (intensity) is spatially localized and this pattern shifts at the speed of light. The emitted photon exhibits classical-like phase properties in the intensity expectation value when it "interferes with itself" after reflection. The phase properties of the emitted radiation are also evident at times sufficiently long for the radiation to have returned to the emitting atom before the decay of excited atomic state is complete. ©2002 American Association of Physics Teachers.
| History: | Received 21 May 2001; accepted 7 September 2001 |
| Permalink: | http://dx.doi.org/10.1119/1.1417531 |