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One-dimensional motion

Victor Galitski, Boris Karnakov, Vladimir Kogan, and Victor Galitski, Jr.

in Exploring Quantum Mechanics: A Collection of 700+ Solved Problems for Students, Lecturers, and Researchers

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199232710
eISBN:
9780191774973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232710.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter analyzes problems that deal with stationary states in the discrete spectrum; the Schrödinger equation in momentum space (the Green function and integral form of the Schrödinger ... More


Motion in a spherically-symmetric potential

Victor Galitski, Boris Karnakov, Vladimir Kogan, and Victor Galitski, Jr.

in Exploring Quantum Mechanics: A Collection of 700+ Solved Problems for Students, Lecturers, and Researchers

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199232710
eISBN:
9780191774973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232710.003.0004
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter covers problems that deal with discrete spectrum states in central fields; low-energy states; symmetries of the Coulomb problem; and systems with axial symmetry.


Perturbation theory; Variational method; Sudden and adiabatic theory

Victor Galitski, Boris Karnakov, Vladimir Kogan, and Victor Galitski, Jr.

in Exploring Quantum Mechanics: A Collection of 700+ Solved Problems for Students, Lecturers, and Researchers

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199232710
eISBN:
9780191774973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232710.003.0008
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter analyzes problems that deal with stationary perturbation theory (discrete spectrum); variational method; stationary perturbation theory (continuous spectrum); non-stationary perturbation ... More


Capacity and Compactness Criteria

D. E. Edmunds and W. D. Evans

in Spectral Theory and Differential Operators

Published in print:
2018
Published Online:
September 2018
ISBN:
9780198812050
eISBN:
9780191861130
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198812050.003.0008
Subject:
Mathematics, Pure Mathematics

In this chapter, necessary and sufficient conditions are derived for the Poincaré inequality to hold, for the embedding of W01,p(Ω) in Lp(Ω‎) to be compact, and for a self-adjoint realization of − ... More


Boundary Cohomology

Günter Harder and A. Raghuram

in Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions: (AMS-203)

Published in print:
2019
Published Online:
September 2020
ISBN:
9780691197890
eISBN:
9780691197937
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691197890.003.0004
Subject:
Mathematics, Number Theory

This chapter discusses some relevant details of the cohomology of the boundary of the Borel–Serre compactification of the locally symmetric space SGKf. It first illustrates a spectral sequence ... More


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