Proper quantization rule as a good candidate to semiclassical quantization rules

2011 ◽  
Vol 523 (10) ◽  
pp. 771-782 ◽  
Author(s):  
F.A. Serrano ◽  
M. Cruz-Irisson ◽  
S.-H. Dong
Keyword(s):  
Quantization Rule ◽  
Semiclassical Quantization ◽  
Quantization Rules

Remarks on semiclassical quantization rule for broken SUSY

1993 ◽  
Vol 26 (9) ◽  
pp. 2261-2264 ◽  
Author(s):  
A Inomata ◽  
G Junker ◽  
A Suparmi
Keyword(s):  
Quantization Rule ◽  
Semiclassical Quantization

scholarly journals Regular Bohr-Sommerfeld quantization rules for a h-pseudo-differential operator. The method of positive commutators

2016 ◽  
Vol Volume 23 - 2016 - Special... ◽  
Author(s):  
Abdelwaheb Ifa ◽  
Michel Rouleux
Keyword(s):  
Differential Operator ◽  
Gram Matrix ◽  
Pseudo Differential Operator ◽  
Quantization Rule ◽  
International Audience ◽  
Scalar Products ◽  
Quantization Rules

International audience We revisit in this Note the well known Bohr-Sommerfeld quantization rule (BS) for a 1-D Pseudo-differential self-adjoint Hamiltonian within the algebraic and microlocal framework of Helffer and Sjöstrand; BS holds precisely when the Gram matrix consisting of scalar products of some WKB solutions with respect to the " flux norm " is not invertible. Dans le cadre algébrique et microlocal élaboré par Helffer et Sjöstrand, on propose une ré-écriture de la règle de quantification de Bohr-Sommerfeld pour un opérateur auto-adjoint h-Pseudo-différentiel 1-D; elle s'exprime par la non-inversibilité de la matrice de Gram d'un couple de solutions WKB dans une base convenable, pour le produit scalaire associé à la " norme de flux " .

Bohr–Sommerfeld, WKB, and modified semiclassical quantization rules

1986 ◽  
Vol 54 (2) ◽  
pp. 131-134 ◽  
Author(s):  
D. J. W. Geldart ◽  
D. Kiang
Keyword(s):  
Semiclassical Quantization ◽  
Quantization Rules

Exactness of the broken supersymmetric, semiclassical quantization rule

1995 ◽  
Vol 52 (5) ◽  
pp. 4259-4261 ◽  
Author(s):  
N. R. Murali ◽  
T. R. Govindarajan ◽  
Avinash Khare
Keyword(s):  
Quantization Rule ◽  
Semiclassical Quantization

scholarly journals Short-Time Propagators and the Born–Jordan Quantization Rule

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 869 ◽  
Author(s):  
Maurice de Gosson
Keyword(s):  
Quantum Mechanics ◽  
Quantization Scheme ◽  
Action Functional ◽  
Quantization Rule ◽  
Short Time ◽  
Quantization Rules

We have shown in previous work that the equivalence of the Heisenberg and Schrödinger pictures of quantum mechanics requires the use of the Born and Jordan quantization rules. In the present work we give further evidence that the Born–Jordan rule is the correct quantization scheme for quantum mechanics. For this purpose we use correct short-time approximations to the action functional, initially due to Makri and Miller, and show that these lead to the desired quantization of the classical Hamiltonian.

scholarly journals QUANTUM CORRECTIONS TO THE SEMICLASSICAL QUANTIZATION OF THE SU(3) SHELL MODEL

1995 ◽  
Vol 09 (24) ◽  
pp. 3219-3227 ◽  
Author(s):  
V. R. MANFREDI ◽  
L. SALASNICH
Keyword(s):  
Perturbation Theory ◽  
Shell Model ◽  
Semiclassical Approximation ◽  
Energy Levels ◽  
Quantum Corrections ◽  
Numerical Accuracy ◽  
Quantization Rule ◽  
Semiclassical Quantization ◽  
Canonical Perturbation

We apply the canonical perturbation theory to the semi-quantal Hamiltonian of the SU(3) shell model. Then, we use the Einstein–Brillowin–Keller quantization rule to obtain an analytical semi-quantal formula for the energy levels, which is the usual semiclassical one plus quantum corrections. Finally, a test on the numerical accuracy of the semiclassical approximation and of its quantum corrections is performed.

On the exactness of the SUSY semiclassical quantization rule

1987 ◽  
Vol 188 (3) ◽  
pp. 351-352 ◽  
Author(s):  
K. Raghunathan ◽  
M. Seetharaman ◽  
S.S. Vasan
Keyword(s):  
Quantization Rule ◽  
Semiclassical Quantization
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