Bohmian Quantum Mechanics Revisited

By expressing the Schrödinger wave function in the form ψ = R e i S / ℏ , where R and S are real functions, we have shown that the expectation value of S is conserved. The amplitude of the wave (R) is found to satisfy the Schrödinger equation while the phase (S) is related to the energy conservation. Besides the quantum potential that depends on R, viz., V Q = - ℏ 2 2 m ∇ 2 R R , we have obtained a spin potential V S = - S ∇ 2 S m that depends on S which is attributed to the particle spin. The spin force is found to give rise to dissipative viscous force. The quantum potential may be attributed to the interaction between the two subfields S and R comprising the quantum particle. This results in splitting (creation/annihilation) of these subfields, each having a mass m c 2 with an internal frequency of 2 m c 2 / ℏ , satisfying the original wave equation and endowing the particle its quantum nature. The mass of one subfield reflects the interaction with the other subfield. If in Bohmian ansatz R satisfies the Klein-Gordon equation, then S must satisfies the wave equation. Conversely, if R satisfies the wave equation, then S yields the Einstein relativistic energy momentum equation.

Bohmian Quantum Mechanics Revisited

By expressing the Schrödinger wave function in the form ψ = R e i S / ℏ , where R and S are real functions, we have shown that the expectation value of S is conserved. The amplitude of the wave (R) is found to satisfy the Schrödinger equation while the phase (S) is related to the energy conservation. Besides the quantum potential that depends on R, viz., V Q = - ℏ 2 2 m ∇ 2 R R , we have obtained a spin potential V S = - S ∇ 2 S m that depends on S which is attributed to the particle spin. The spin force is found to give rise to dissipative viscous force. The quantum potential may be attributed to the interaction between the two subfields S and R comprising the quantum particle. This results in splitting (creation/annihilation) of these subfields, each having a mass m c 2 with an internal frequency of 2 m c 2 / ℏ , satisfying the original wave equation and endowing the particle its quantum nature. The mass of one subfield reflects the interaction with the other subfield. If in Bohmian ansatz R satisfies the Klein-Gordon equation, then S must satisfies the wave equation. Conversely, if R satisfies the wave equation, then S yields the Einstein relativistic energy momentum equation.

Gravitational reduction of the wave function based on Bohmian quantum potential

In objective gravitational reduction of the wave function of a quantum system, the classical limit of the system is obtained in terms of the objective properties of the system. On the other hand, in Bohmian quantum mechanics the usual criterion for getting classical limit is the vanishing of the quantum potential or the quantum force of the system, which suffers from the lack of an objective description. In this regard, we investigated the usual criterion of getting the classical limit of a free particle in Bohmian quantum mechanics. Then we argued how it is possible to have an objective gravitational classical limit related to the Bohmian mechanical concepts like quantum potential or quantum force. Also we derived a differential equation related to the wave function reduction. An interesting connection will be made between Bohmian mechanics and gravitational concepts.

Quantum effects on the deflection of light and the Gauss–Bonnet theorem

In this paper, we apply the Gauss–Bonnet (GB) theorem to calculate the deflection angle by a quantum-corrected Schwarzschild black hole in the weak limit approximation. In particular, we calculate the light deflection by two types of quantum-corrected black holes: the renormalization group improved Schwarzschild solution and the quantum-corrected Schwarzschild solution in Bohmian quantum mechanics. We start from the corresponding optical metrics to use then the GB theorem and calculate the Gaussian curvature in both cases. We calculate the leading terms of the deflection angle and show that quantum corrections modify the deflection angle in both solutions. Finally by performing geodesics calculations we show that GB method gives exact results in leading-order terms.

From the Universe to Subsystems: Why Quantum Mechanics Appears More Stochastic than Classical Mechanics

By means of the examples of classical and Bohmian quantum mechanics, we illustrate the well-known ideas of Boltzmann as to how one gets from laws defined for the universe as a whole the dynamical relations describing the evolution of subsystems. We explain how probabilities enter into this process, what quantum and classical probabilities have in common and where exactly their difference lies.

ONE DIMENSIONAL SCATTERING PROBLEM IN BOHMIAN QUANTUM MECHANICS

According to Standard Quantum Mechanics (SQM), known as the Copenhagen Interpretation, the complete description of a system of particles is provided by its wave function. However, in the de Broglie-Bohm theory of Bohmian Quantum Mechanics (BQM), the additional element which is introduced apart from the wave function is the particle position, conceived in the classical sense as pursuing a definite continuous track in space-time. In BQM formulation, depending on the configuration of the potential barrier and the energy of the packet, the particle trajectories have been shown to take distinct paths. We will consider several barrier heights and show that in a Bohmian interpretation of the problem, there is no such thing as Quantum Tunnelling.