منابع مشابه
Quantum Hamilton-Jacobi equation
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 generating function of a canonical transformation that maps any quantum system to a system with a vanishing Hamiltonian. A formal perturbative solution of th...
متن کاملQuantum Hamilton-Jacobi theory.
Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear operator partial differential equation such as the quantum Hamilton-Jacobi equation (QHJE) has hindered progress along this otherwise promising avenue. We over...
متن کاملThe Three-Dimensional Quantum Hamilton-Jacobi Equation and Microstates
In a stationary case and for any potential, we solve the three-dimensional quantum Hamilton-Jacobi equation in terms of the solutions of the corresponding Schrödinger equation. Then, in the case of separated variables, by requiring that the conjugate momentum be invariant under any linear transformation of the solutions of the Schrödinger equation used in the reduced action, we clearly identify...
متن کاملClifford Algebras and the Dirac-Bohm Quantum Hamilton-Jacobi Equation
In this paper we show how the dynamics of the Schrödinger, Pauli and Dirac particles can be described entirely within the hierarchy of Clifford algebras, C1,3, C3,0, and C0,1. There is no need to introduce vectors in Hilbert space, but that option is always available. The state of the quantum process is characterised by algebraic bilinear invariants of the first and second kind. We show the bil...
متن کاملEquivalence Principle, Planck Length and Quantum Hamilton–Jacobi Equation
The Quantum Stationary HJ Equation (QSHJE) that we derived from the equivalence principle, gives rise to initial conditions which cannot be seen in the Schrödinger equation. Existence of the classical limit leads to a dependence of the integration constant l = l1 + il2 on the Planck length. Solutions of the QSHJE provide a trajectory representation of quantum mechanics, which, unlike Bohm’s the...
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ژورنال
عنوان ژورنال: Physical Review Letters
سال: 1998
ISSN: 0031-9007,1079-7114
DOI: 10.1103/physrevlett.80.4366