Zworski, Maciej
Semiclassical analysis - Providence, R.I. : American Mathematical Society, c2012. - xii, 431 p. ; - Graduate studies in mathematics ; .
Semiclassical analysis provides PDE techniques based on the classical-quantum (particle-wave) correspondence. These techniques include such well-known tools as geometric optics and the Wentzel–Kramers–Brillouin approximation. Examples of problems studied in this subject are high energy eigenvalue asymptotics and effective dynamics for solutions of evolution equations. From the mathematical point of view, semiclassical analysis is a branch of microlocal analysis which, broadly speaking, applies harmonic analysis and symplectic geometry to the study of linear and nonlinear PDE. The book is intended to be a graduate level text introducing readers to semiclassical and microlocal methods in PDE. It is augmented in later chapters with many specialized advanced topics which provide a link to current research literature.
9781470425845
2012010649
Quantum theory
Differential equations, Partial
Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with quantum mechanics.
Quantum theory -- General mathematical topics and methods in quantum theory -- Semiclassical techniques, including WKB and Maslov methods.
Partial differential equations -- Pseudodifferential operators and other generalizations of partial differential operators -- Pseudodifferential operators.
Partial differential equations -- Pseudodifferential operators and other generalizations of partial differential operators -- Fourier integral operators.
Partial differential equations -- Spectral theory and eigenvalue problems -- Asymptotic distribution of eigenvalues and eigenfunctions.
Quantum theory -- General quantum mechanics and problems of quantization -- Geometry and quantization, symplectic methods.
515 / ZWO/S
Semiclassical analysis - Providence, R.I. : American Mathematical Society, c2012. - xii, 431 p. ; - Graduate studies in mathematics ; .
Semiclassical analysis provides PDE techniques based on the classical-quantum (particle-wave) correspondence. These techniques include such well-known tools as geometric optics and the Wentzel–Kramers–Brillouin approximation. Examples of problems studied in this subject are high energy eigenvalue asymptotics and effective dynamics for solutions of evolution equations. From the mathematical point of view, semiclassical analysis is a branch of microlocal analysis which, broadly speaking, applies harmonic analysis and symplectic geometry to the study of linear and nonlinear PDE. The book is intended to be a graduate level text introducing readers to semiclassical and microlocal methods in PDE. It is augmented in later chapters with many specialized advanced topics which provide a link to current research literature.
9781470425845
2012010649
Quantum theory
Differential equations, Partial
Partial differential equations -- Equations of mathematical physics and other areas of application -- PDEs in connection with quantum mechanics.
Quantum theory -- General mathematical topics and methods in quantum theory -- Semiclassical techniques, including WKB and Maslov methods.
Partial differential equations -- Pseudodifferential operators and other generalizations of partial differential operators -- Pseudodifferential operators.
Partial differential equations -- Pseudodifferential operators and other generalizations of partial differential operators -- Fourier integral operators.
Partial differential equations -- Spectral theory and eigenvalue problems -- Asymptotic distribution of eigenvalues and eigenfunctions.
Quantum theory -- General quantum mechanics and problems of quantization -- Geometry and quantization, symplectic methods.
515 / ZWO/S