A Note on Forming the Correct Schrödinger Equation by Correspondence with Classical Mechanics

The derivation of the time dependent Schrödinger equation with transversal and longitudinal relaxation, as the quantum mechanical analog of the classical Landau-Lifshitz-Bloch equation, has been described. Starting from the classical Landau-Lifshitz-Bloch equation the transition to quantum mechanics has been performed and the corresponding von-Neumann equation deduced. In a second step the time Schrödinger equation has been derived. Analytical proofs and computer simulations show the correctness and applicability of the derived Schrödinger equation.The derivation of the time dependent Schrödinger equation with transversal and longitudinal relaxation, as the quantum mechanical analog of the classical Landau-Lifshitz-Bloch equation, has been described. Starting from the classical Landau-Lifshitz-Bloch equation the transition to quantum mechanics has been performed and the corresponding von-Neumann equation deduced. In a second step the time Schrödinger equation has been derived. Analytical proofs and computer simulations show the correctness and applicability of the derived Schrödinger equation.

arXiv:1607.06184Journal of Physics Condensed MatterAug 5, 201610 citations

Theoretical Note: Derivation of the Schrödinger Equation from the Chronodynamic Euler State

Ambiel da Silva, Marcelo

In the framework of Chronodynamic Cosmology (CDC), the vacuum is defined as a physical superfluid (Psi). If this premise is correct, the fundamental equations of Quantum Mechanics must be derivable from Hydrodynamics. In this note, we perform the Madelung Transformation to demonstrate that the Schrödinger Equation is mathematically equivalent to the Euler Equation for an inviscid, compressible fluid subjected to a specific internal pressure potential. This derivation suggests that "Quantum Potential" (Q) is the hydrostatic pressure of the Time-Fluid, and that "Wavefunction Collapse" is a phase transition from an inviscid (superfluid) state to a viscous (classical) state.In the framework of Chronodynamic Cosmology (CDC), the vacuum is defined as a physical superfluid (Psi). If this premise is correct, the fundamental equations of Quantum Mechanics must be derivable from Hydrodynamics. In this note, we perform the Madelung Transformation to demonstrate that the Schrödinger Equation is mathematically equivalent to the Euler Equation for an inviscid, compressible fluid subjected to a specific internal pressure potential. This derivation suggests that "Quantum Potential" (Q) is the hydrostatic pressure of the Time-Fluid, and that "Wavefunction Collapse" is a phase transition from an inviscid (superfluid) state to a viscous (classical) state.

Nov 25, 20250 citations

Notes on quantum mechanics: the Schrodinger Equation

Nielsen, M. P., Laugesen, Jacob, Sanjayan, J. G.

Jan 1, 20010 citations

A Correction: Some Remarks Concerning Schrodinger's Wave Equation

Geo. D. Birkhoff

Proceedings of the National Academy of SciencesApr 1, 19330 citations

Charged Schrödinger particle in a c -number radiation field

Tadashi Toyoda, K. Wildermuth

We formulate a method to derive the time-dependent Schr\"odinger equation which describes the interaction of an electron with a $c$ -number radiation field. To obtain this semiclassical approximation from the complete quantum-mechanical formulation we use the corresponding Schr\"odinger equation in its projection form, which is an extension of the Hill-Wheeler generator coordinate method. For the basis states of the radiation field we introduce a complete, but not overcomplete, subset of coherent states, which were found by von Neumann and whose proof of completeness was given by Bargmann et al. and Perdomov. We find that the conventional overcomplete continuous coherent states are not suitable for the projection form of the Schr\"odinger equation. The method also allows one to calculate quantum-mechanical correction terms systematically.We formulate a method to derive the time-dependent Schr\"odinger equation which describes the interaction of an electron with a $c$-number radiation field. To obtain this semiclassical approximation from the complete quantum-mechanical formulation we use the corresponding Schr\"odinger equation in its projection form, which is an extension of the Hill-Wheeler generator coordinate method. For the basis states of the radiation field we introduce a complete, but not overcomplete, subset of coherent states, which were found by von Neumann and whose proof of completeness was given by Bargmann et al. and Perdomov. We find that the conventional overcomplete continuous coherent states are not suitable for the projection form of the Schr\"odinger equation. The method also allows one to calculate quantum-mechanical correction terms systematically.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsNov 15, 19806 citations

We formulate a method to derive the time-dependent Schr\"odinger equation which describes the interaction of an electron with a

c

-number radiation field. To obtain this semiclassical approximation from the complete quantum-mechanical formulation we use the corresponding Schr\"odinger equation in its projection form, which is an extension of the Hill-Wheeler generator coordinate method. For the basis states of the radiation field we introduce a complete, but not overcomplete, subset of coherent states, which were found by von Neumann and whose proof of completeness was given by Bargmann et al. and Perdomov. We find that the conventional overcomplete continuous coherent states are not suitable for the projection form of the Schr\"odinger equation. The method also allows one to calculate quantum-mechanical correction terms systematically.