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Physical Review A

Addendum to "Time-dependent variational principle with constraints for parametrized wave functions" (4 pages)

K. Ohta

Published Jan 1, 2006• 0 citations
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Addendum to “Time-dependent variational principle with constraints for parametrized wave functions”

Katsuhisa Ohta

The sensitivity analysis for the time-dependent variational principle (TDVP) with constraints for parametrized wave functions [K. Ohta, Phys. Rev. A 70, 022503 (2004)] is investigated to assess the geodesic deviation caused by external parameters. The constraints for the sensitivity functions, inherited from the TDVP, are dealt with their consistency conditions. As an example of the sensitivity analysis, the geodesic deviation in the neighborhood of stationary states is investigated for general wave functions.

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Nonsingular constraints in time‐dependent variational principle for parametrized wave functions

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Abstract In this work, we consider two conditions required for the nonsingularity of constraints in the time‐dependent variational principle (TDVP) for parametrized wave functions. One is the regularity condition which assures the static nonsingularity of the constraint surface. The other condition is the second‐class condition of constraints which assures the dynamic nonsingularity of the constraint surface with a symplectic metric. For analytic wave functions for complex TDVP‐parameters, the regularity and the second‐class conditions become equivalent. The second‐class condition for expectation values is reduced to the noncommutability of the corresponding quantum operators. The symplectic singularity of the equation of motion of TDVP is also shown to be a local breakdown of the second‐class condition in an extended canonical phase‐space. © 2012 Wiley Periodicals, Inc.

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Addendum to "Phenomenological Derivation of the Schrodinger Equation"

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Progress in physics•Apr 1, 2014•1 citation
The sensitivity analysis for the time-dependent variational principle (TDVP) with constraints for parametrized wave functions [K. Ohta, Phys. Rev. A 70, 022503 (2004)] is investigated to assess the geodesic deviation caused by external parameters. The constraints for the sensitivity functions, inherited from the TDVP, are dealt with their consistency conditions. As an example of the sensitivity analysis, the geodesic deviation in the neighborhood of stationary states is investigated for general wave functions.
Abstract In this work, we consider two conditions required for the nonsingularity of constraints in the time‐dependent variational principle (TDVP) for parametrized wave functions. One is the regularity condition which assures the static nonsingularity of the constraint surface. The other condition is the second‐class condition of constraints which assures the dynamic nonsingularity of the constraint surface with a symplectic metric. For analytic wave functions for complex TDVP‐parameters, the regularity and the second‐class conditions become equivalent. The second‐class condition for expectation values is reduced to the noncommutability of the corresponding quantum operators. The symplectic singularity of the equation of motion of TDVP is also shown to be a local breakdown of the second‐class condition in an extended canonical phase‐space. © 2012 Wiley Periodicals, Inc.