Matches in SemOpenAlex for { <https://semopenalex.org/work/W2168695810> ?p ?o ?g. }
Showing items 1 to 86 of
86
with 100 items per page.
- W2168695810 abstract "In this and the next chapter, we begin a study of the behavior of the spectrum of Schrodinger operators in the semiclassical regime. There is much literature on these topics, and we provide an outline in the Notes to this chapter. The material here follows a part of the work of Simon [Sim5]. In quantum mechanics, the Laplacian plays the role of the energy of a free particle. But, the Laplacian apparently has the dimensions of (length)-2. This is because in our discussions of the Schrodinger operator, we have chosen to work in simple units in which the mass m = 1/2 and Planck’s constant h is taken to be 2π. In these units, the coefficient of the kinetic energy H 0 = -△ is 1. If we restore these constants, the actual differential operator in quantum mechanics representing the energy of a free particle is. The Planck constant h is approximately 6.624 x 10-27 ergs/sec. This is very small except on atomic scales. That is, the length scales over which quantum effects are important depend on h (for example, the Compton wavelength of an electron or the Bohr radius of an atom). This observation provides us with one way to understand the transition from classical to quantum phenomena. We consider quantum theory in which Planck’s constant has been replaced by a small parameter. We then try to understand quantum mechanics in terms of the classical theory obtained as the limit of this quantum theory as the parameter is taken to zero. We call this limit h = 0 the classical limit since all quantum effects have been suppressed. The regime in which this parameter is nonzero, but taken arbitrarily small, is called the semiclassical regime. In this regime, the behavior of the quantum mechanical system should be dominated by the limiting h = 0 classical system." @default.
- W2168695810 created "2016-06-24" @default.
- W2168695810 creator A5004954975 @default.
- W2168695810 creator A5057592767 @default.
- W2168695810 date "1996-01-01" @default.
- W2168695810 modified "2023-09-24" @default.
- W2168695810 title "Semiclassical Analysis of Schrödinger Operators I: The Harmonic Approximation" @default.
- W2168695810 doi "https://doi.org/10.1007/978-1-4612-0741-2_11" @default.
- W2168695810 hasPublicationYear "1996" @default.
- W2168695810 type Work @default.
- W2168695810 sameAs 2168695810 @default.
- W2168695810 citedByCount "0" @default.
- W2168695810 crossrefType "book-chapter" @default.
- W2168695810 hasAuthorship W2168695810A5004954975 @default.
- W2168695810 hasAuthorship W2168695810A5057592767 @default.
- W2168695810 hasConcept C104240894 @default.
- W2168695810 hasConcept C104317684 @default.
- W2168695810 hasConcept C108568745 @default.
- W2168695810 hasConcept C118697519 @default.
- W2168695810 hasConcept C121332964 @default.
- W2168695810 hasConcept C147120987 @default.
- W2168695810 hasConcept C158448853 @default.
- W2168695810 hasConcept C165700671 @default.
- W2168695810 hasConcept C166126730 @default.
- W2168695810 hasConcept C17020691 @default.
- W2168695810 hasConcept C185592680 @default.
- W2168695810 hasConcept C192638945 @default.
- W2168695810 hasConcept C194800363 @default.
- W2168695810 hasConcept C194975256 @default.
- W2168695810 hasConcept C197111296 @default.
- W2168695810 hasConcept C37387333 @default.
- W2168695810 hasConcept C535169671 @default.
- W2168695810 hasConcept C55493867 @default.
- W2168695810 hasConcept C62520636 @default.
- W2168695810 hasConcept C68030841 @default.
- W2168695810 hasConcept C84114770 @default.
- W2168695810 hasConcept C86339819 @default.
- W2168695810 hasConceptScore W2168695810C104240894 @default.
- W2168695810 hasConceptScore W2168695810C104317684 @default.
- W2168695810 hasConceptScore W2168695810C108568745 @default.
- W2168695810 hasConceptScore W2168695810C118697519 @default.
- W2168695810 hasConceptScore W2168695810C121332964 @default.
- W2168695810 hasConceptScore W2168695810C147120987 @default.
- W2168695810 hasConceptScore W2168695810C158448853 @default.
- W2168695810 hasConceptScore W2168695810C165700671 @default.
- W2168695810 hasConceptScore W2168695810C166126730 @default.
- W2168695810 hasConceptScore W2168695810C17020691 @default.
- W2168695810 hasConceptScore W2168695810C185592680 @default.
- W2168695810 hasConceptScore W2168695810C192638945 @default.
- W2168695810 hasConceptScore W2168695810C194800363 @default.
- W2168695810 hasConceptScore W2168695810C194975256 @default.
- W2168695810 hasConceptScore W2168695810C197111296 @default.
- W2168695810 hasConceptScore W2168695810C37387333 @default.
- W2168695810 hasConceptScore W2168695810C535169671 @default.
- W2168695810 hasConceptScore W2168695810C55493867 @default.
- W2168695810 hasConceptScore W2168695810C62520636 @default.
- W2168695810 hasConceptScore W2168695810C68030841 @default.
- W2168695810 hasConceptScore W2168695810C84114770 @default.
- W2168695810 hasConceptScore W2168695810C86339819 @default.
- W2168695810 hasLocation W21686958101 @default.
- W2168695810 hasOpenAccess W2168695810 @default.
- W2168695810 hasPrimaryLocation W21686958101 @default.
- W2168695810 hasRelatedWork W1034804916 @default.
- W2168695810 hasRelatedWork W1613077521 @default.
- W2168695810 hasRelatedWork W1623231372 @default.
- W2168695810 hasRelatedWork W1644428999 @default.
- W2168695810 hasRelatedWork W1652263410 @default.
- W2168695810 hasRelatedWork W1936705622 @default.
- W2168695810 hasRelatedWork W197382624 @default.
- W2168695810 hasRelatedWork W1977811489 @default.
- W2168695810 hasRelatedWork W1985199773 @default.
- W2168695810 hasRelatedWork W2076539253 @default.
- W2168695810 hasRelatedWork W2899453666 @default.
- W2168695810 hasRelatedWork W2953196898 @default.
- W2168695810 hasRelatedWork W2980880813 @default.
- W2168695810 hasRelatedWork W3046834568 @default.
- W2168695810 hasRelatedWork W3101294327 @default.
- W2168695810 hasRelatedWork W3165694556 @default.
- W2168695810 hasRelatedWork W575831615 @default.
- W2168695810 hasRelatedWork W95073371 @default.
- W2168695810 hasRelatedWork W2110699846 @default.
- W2168695810 hasRelatedWork W2522721766 @default.
- W2168695810 isParatext "false" @default.
- W2168695810 isRetracted "false" @default.
- W2168695810 magId "2168695810" @default.
- W2168695810 workType "book-chapter" @default.