Related papers: Quantum Potential Via General Hamilton - Jacobi Eq…
This is the second of the two related papers analysing origins and possible explanations of a paradoxical phenomenon of the quantum potential (QP). It arises in quantum mechanics'(QM) of a particle in the Riemannian $n$-dimensional…
The first of the two related papers analising and explaining the origin, manifestations and parodoxical features of the quantum potential (QP) from the non-relativistic and relativistic point of view. QP arises in the quantum Hamiltonian,…
The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space…
Quantum Hamilton-Jacobi quantization scheme uses the singularity structure of the potential of a quantum mechanical system to generate its eigenspectrum and eigenfunctions, and its efficacy has been demonstrated for several well known…
The quantum potential approach makes it possible to construct a complementary picture of quantum mechanical evolution which reminds classical equation of motion. The only difference as compared to equations of motion for the underlying…
We use the quantum potential approach to analyse the quantum cosmological model of the universe. The quantum potential arises from exact solutions of the full Wheeler-De Witt equation.
In this thesis the quantum Hamilton - Jacobi (QHJ) formalism is used for (i) potentials which exhibit different spectra for different ranges of the potential parameters, (ii) exactly solvable (ES) periodic potentials (iii) quasi - exactly…
It is well known in classical mechanics that, the frequencies of a periodic system can be obtained rather easily through the action variable, without completely solving the equation of motion. The equivalent quantum action variable…
Commutativity of the diagram of the maps connecting three one--particle state, implied by the Equivalence Postulate (EP), gives a cocycle condition which unequivocally leads to the quantum Hamilton--Jacobi equation. Energy quantization is a…
It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a…
In this article, we develop quantum mechanics upon the framework of the quantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger point of view and the Hamilton-Jacobi point of view are fully equivalent in their…
We suggest that quantum mechanics and gravity are intimately related. In particular, we investigate the quantum Hamilton-Jacobi equation in the case of two free particles and show that the quantum potential, which is attractive, may…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…
The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the…
We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton-Jacobi equation. While in the classically forbidden regions these quantum quantities directly tend to the…
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of Covariant Quantum-Gravity (CQG-theory). The treatment is founded on the recently-identified Hamiltonian structure…
In this article we review some results obtained from a generalization of quantum mechanics obtained from modification of the canonical commutation relation $[q,p]={\rm i}\hbar$. We present some new results concerning relativistic…
A necessary and sufficient condition for a parameter transformation that leaves invariant the energy of a one dimensional autonomous system is obtained. Using a parameter transformation the Hamilton-Jacobi equation is solved by a…
Canonical transformations using the idea of quantum generating functions are applied to construct a quantum Hamilton-Jacobi theory, based on the analogy with the classical case. An operator and a c-number forms of the time-dependent quantum…
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…