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The mathematics of superoscillations /
"In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed that superoscillations naturally arise when dealing with weak values, a notion that provides a fundamentally differ...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2017.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1174. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title page; Chapter 1. Introduction; Chapter 2. Physical motivations; 2.1. Overview; 2.2. Von Neumann measurements; 2.3. Weak values and weak measurements
- the main idea; 2.4. Weak values and weak measurements
- mathematical aspects; 2.5. Large weak values and superoscillations; Chapter 3. Basic mathematical properties of superoscillating sequences; 3.1. Superoscillating sequences; 3.2. Test functions and their Fourier transforms; 3.3. Approximations of functions in (ℝ); Chapter 4. Function spaces of holomorphic functions with growth; 4.1. Analytically Uniform spaces
- 4.2. Convolutors on Analytically Uniform spaces4.3. Dirichlet series; Chapter 5. Schrödinger equation and superoscillations; 5.1. Schrödinger equation for the free particle; 5.2. Approximation by gaussians and persistence of superoscillations; 5.3. Quantum harmonic oscillator; Chapter 6. Superoscillating functions and convolution equations; 6.1. Convolution operators for generalized Schrödinger equations; 6.2. Formal solutions to Cauchy problems for linear constant coefficients differential equations; 6.3. Differential equations of non-Kowalevski type.
- 6.4. An application to the harmonic oscillatorChapter 7. Superoscillating functions and operators; 7.1. A quick review on operators; 7.2. Superoscillations and operators; Chapter 8. Superoscillations in (3); 8.1. The weak value of the operator exp( ℒ_{ }\myupn ); 8.2. Asymptotic expansion for the Wigner functions; Bibliography; Index; Back Cover