Canonical transformations and their representations in quantum mechanics

1977 ◽  
pp. 469-481
Author(s):  
M. Moshinsky
Keyword(s):  
Quantum Mechanics ◽  
Canonical Transformations

On the symplectically invariant variational principle and generating functions

1990 ◽  
Vol 431 (1883) ◽  
pp. 403-417 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Variational Principle ◽  
Generating Function ◽  
Generating Functions ◽  
Geometric Approach ◽  
Canonical Transformations ◽  
Weyl Transform ◽  
Analogous Relation ◽  
Definition Of ◽  
Symplectic Invariance

The generating function for canonical transformations derived by Marinov has the important property of symplectic invariance (i. e. under linear canonical transformations). However, a more geometric approach to the rederivation of this function from the variational principle reveals that it is not free from caustic singularities after all. These singularities can be avoided without breaking the symplectic invariance by the definition of a complementary generating function bearing an analogous relation to the Woodward ambiguity function in telecommunications theory as that tying Marinov’s function to the Wigner function and the Weyl transform in quantum mechanics. Marinov’s function is specially apt to describe canonical transformations close to the identity, but breaks down for reflections through a point in phase space, easily described by the new generating function.

scholarly journals Canonical transformations in quantum mechanics

2013 ◽  
Vol 331 ◽  
pp. 70-96 ◽  
Author(s):  
Maciej Błaszak ◽  
Ziemowit Domański
Keyword(s):  
Quantum Mechanics ◽  
Canonical Transformations

Canonical transformations to action and angle variables and their representations in quantum mechanics

1980 ◽  
Vol 127 (2) ◽  
pp. 458-477 ◽  
Author(s):  
J Deenen ◽  
M Moshinsky ◽  
T.H Seligman
Keyword(s):  
Quantum Mechanics ◽  
Canonical Transformations

Nonbijective canonical transformations and their representation in quantum mechanics

1978 ◽  
Vol 19 (3) ◽  
pp. 683-693 ◽  
Author(s):  
P. Kramer ◽  
M. Moshinsky ◽  
T. H. Seligman
Keyword(s):  
Quantum Mechanics ◽  
Canonical Transformations

scholarly journals QUANTUM CANONICAL TRANSFORMATIONS IN WEYL–WIGNER–GROENEWOLD–MOYAL FORMALISM

2009 ◽  
Vol 24 (24) ◽  
pp. 4573-4587 ◽  
Author(s):  
TEKİN DERELİ ◽  
TUĞRUL HAKİOĞLU ◽  
ADNAN TEĞMEN
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Generating Function ◽  
Canonical Transformation ◽  
Star Product ◽  
Product Form ◽  
Canonical Transformations ◽  
Exponential Form ◽  
Alternative Approach ◽  
Point Transformations

A conjecture in quantum mechanics states that any quantum canonical transformation can decompose into a sequence of three basic canonical transformations; gauge, point and interchange of coordinates and momenta. It is shown that if one attempts to construct the three basic transformations in star-product form, while gauge and point transformations are immediate in star-exponential form, interchange has no correspondent, but it is possible in an ordinary exponential form. As an alternative approach, it is shown that all three basic transformations can be constructed in the ordinary exponential form and that in some cases this approach provides more useful tools than the star-exponential form in finding the generating function for given canonical transformation or vice versa. It is also shown that transforms of c-number phase space functions under linear–nonlinear canonical transformations and intertwining method can be treated within this argument.

Canonical Transformations and Quantum Mechanics

1973 ◽  
Vol 25 (2) ◽  
pp. 193-212 ◽  
Author(s):  
Marcos Moshinsky
Keyword(s):  
Quantum Mechanics ◽  
Canonical Transformations
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