DOI: 10.1002/9780470142899.ch4. Semiclassical Calculation of Quantum Mechanical Wavefunctions

Semiclassical Calculation of Quantum Mechanical Wavefunctions

10.1002/9780470142899.ch4

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Wiley

Advances in Chemical Physics (311)

Bibliography

Delos, J. B. (1986). Semiclassical Calculation of Quantum Mechanical Wavefunctions. Advances in Chemical Physics, 161â214. Portico.

Authors 1

J. B. Delos (first)

References 50 Referenced 78

{'key': 'e_1_2_1_2_2', 'volume-title': 'An Introduction to Phase‐Integral Methods', 'author': 'Heading J.', 'year': '1962'} / An Introduction to Phase‐Integral Methods by Heading J. (1962)
{'key': 'e_1_2_1_3_2', 'first-page': '222', 'volume-title': 'Quantum Mechanics', 'author': 'Messiah A.', 'year': '1964'} / Quantum Mechanics by Messiah A. (1964)
{'key': 'e_1_2_1_3_3', 'first-page': '158', 'volume-title': 'Quantum Mechanics', 'author': 'Landau L. D.', 'year': '1965'} / Quantum Mechanics by Landau L. D. (1965)
10.1016/0009-2614(70)80164-6
10.1063/1.1675449
10.1063/1.1676866
10.1039/dc9735500034
10.1063/1.1675732
10.1063/1.430777
10.1063/1.1674275
10.1063/1.1674839
10.1063/1.1678610
10.1063/1.1677086
10.1016/0003-4916(58)90032-0
10.1016/0003-4916(60)90061-0
10.1016/0003-4916(65)90245-9
10.1103/PhysRev.174.152
10.1103/PhysRev.188.236
10.1103/PhysRevA.1.1150
10.1080/00268977600100041
10.1080/00268977300102421
10.1080/00268977400100771
10.1080/00018737600101342
10.1063/1.430620
10.1063/1.442382
10.1063/1.438727
10.1063/1.442548
MF (ref. 6) cite for example papers written in Russian by Maslov (1961‐1963) Arnold (1967) Kicherenko (1969) Fedoriuk (1971) and Weinberg (1975).
{'key': 'e_1_2_1_5_3', 'volume-title': 'Théorie des Perturbations et Methodes Asymptotiques', 'author': 'Maslov V. P.', 'year': '1972'} / Théorie des Perturbations et Methodes Asymptotiques by Maslov V. P. (1972)
10.1063/1.1678259
{'key': 'e_1_2_1_6_3', 'first-page': '1', 'volume-title': 'Advances in Chemical Physics', 'author': 'Percival I.', 'year': '1977'} / Advances in Chemical Physics by Percival I. (1977)
10.1007/978-94-009-8410-3
{'key': 'e_1_2_1_8_2', 'first-page': 'XX', 'author': 'Knudson S. K.', 'year': '1985', 'journal-title': 'J. Chem. Phys.'} / J. Chem. Phys. by Knudson S. K. (1985)
{'key': 'e_1_2_1_9_2', 'volume-title': 'Classical Mechanics', 'author': 'Goldstein H.', 'year': '1980'} / Classical Mechanics by Goldstein H. (1980)
{'key': 'e_1_2_1_10_2', 'volume-title': 'Methods of Mathematical Physics', 'author': 'Courant R.', 'year': '1966'} / Methods of Mathematical Physics by Courant R. (1966)
{'key': 'e_1_2_1_10_3', 'volume-title': 'Principles of Optics', 'author': 'Born M.', 'year': '1980'} / Principles of Optics by Born M. (1980)
If we were being more strict about scattering theory we would note that we are supposed to take the limit as Z0→‐∞ and then we would discover that lim z0→‐x S(X Z) does not exist. The quantity that has a limit is S(X Z) ‐ S*(X Z) where S*(X Z) is the function obtained by the stated rules from trajectories of theunperturbedHamiltonian (P2x+P2z)/2M.
The statement that Ψ is a solution “to orderh” means that the term proportional to h in (3.3) has been neglected.
{'key': 'e_1_2_1_13_2', 'volume-title': 'Selected Problems in Quantum Mechanics', 'author': 'ter Haar D.', 'year': '1965'} / Selected Problems in Quantum Mechanics by ter Haar D. (1965)
Here our presentation differs somewhat from that given by MF. They give a (quite abstract) geometrical definition of a Lagrangian manifold and then they establish as theorems the properties that we call definitions.
10.1007/BF01075861
Our definition of μ is consistent with MF (definition 7.7) and their example given on p. 146. It has the opposite sign from their definition 7.4 and their example on p. 144. MF also define another index that they call γ but its definition (MF 7.2) is inconsistent with its later usage (MF 8.2). Our indexvcorresponds to the γ that appears in (MF 8.2) and differs by a sign from that in (MF 7.2).
This theorem holds if the manifold is connected in such a way that for any closed path 𝓁con the manifold fcP · dq = 0 and μ (𝓁c) = 0. The manifolds involved in this review have this property.
The word “typical” can be given a precise definition and it has the same meaning here that it has in catastrophe theory. Not all Lagrange manifolds are typical but the ones that are not typical arise from some unusual aspect of dynamics (such as a special symmetry property) and in general a small perturbation applied to an unusual manifold will convert it into a typical one.
{'key': 'e_1_2_1_19_2', 'volume-title': 'Structural Stability and Morphogenesis', 'author': 'Thom R.', 'year': '1975'} / Structural Stability and Morphogenesis by Thom R. (1975)
{'key': 'e_1_2_1_20_2', 'first-page': '269', 'volume-title': 'A Treatise on Analytical Dynamics', 'author': 'Pars L. A.', 'year': '1965'} / A Treatise on Analytical Dynamics by Pars L. A. (1965)
{'key': 'e_1_2_1_21_2', 'first-page': '65', 'volume-title': 'Catastrophe Theory and Its Applications', 'author': 'Poston T. I.', 'year': '1978'} / Catastrophe Theory and Its Applications by Poston T. I. (1978)
10.1017/S0305004100032655
{'key': 'e_1_2_1_23_2', 'volume-title': 'Calculus on Manifolds', 'author': 'Spivak M.', 'year': '1965'} / Calculus on Manifolds by Spivak M. (1965)
10.1007/978-1-4757-1693-1

Dates

Type	When
Created	18 years, 5 months ago (March 14, 2007, 4:22 p.m.)
Deposited	2 years ago (Aug. 26, 2023, 1:55 p.m.)
Indexed	1 year ago (Aug. 2, 2024, 8:41 a.m.)
Issued	39 years, 8 months ago (Jan. 1, 1986)
Published	39 years, 8 months ago (Jan. 1, 1986)
Published Online	18 years, 5 months ago (March 14, 2007)
Published Print	39 years, 8 months ago (Jan. 1, 1986)

Funders 0

None

BibTeX

@misc{Delos_1986, title={Semiclassical Calculation of Quantum Mechanical Wavefunctions}, ISBN={9780470142899}, ISSN={1934-4791}, url={http://dx.doi.org/10.1002/9780470142899.ch4}, DOI={10.1002/9780470142899.ch4}, journal={Advances in Chemical Physics}, publisher={Wiley}, author={Delos, J. B.}, year={1986}, month=jan, pages={161–214} }

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