Bohmian mechanics without pilot waves

Poirier, Bill

doi:10.1016/j.chemphys.2009.12.024

Cited by 62 publications

(90 citation statements)

References 56 publications

(131 reference statements)

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“…In particular, a quantum state can be represented as an ensemble of realvalued quantum trajectories, satisfying a self-contained partial differential equation (PDE). This was shown in a recent paper 7 by one of the authors (Poirier) for both the onedimensional (1D) TISE and TDSE. It transpired that similar work had already been done for the TISE in 1D, 8 the TDSE in 3D, 9 and in greater generality.…”

Section: Introductionmentioning

confidence: 88%

“…(9) (or any uniformizing choice of C), and writing x = ∂x/∂C,ẋ = ∂x/∂t etc., the PDE of Ref. 7 simplifies very substantially to…”

Section: The 1d Time-dependent Casementioning

confidence: 99%

“…7, 1D TIQM states can be represented uniquely with a single trajectory, x(t). The theory is one of a broad class of dynamical laws, for which the Lagrangian and the energy are of the form (1) and (2) are natural generalizations of the wellknown classical forms.…”

Section: The 1d Time-independent Casementioning

confidence: 99%

“…(4)] and (scattering) TIQM states. 7 Any fourth-order ODE can be rewritten as a set of four coupled, first-order ODE's. Remarkably, Eq.…”

Section: The 1d Time-independent Casementioning

confidence: 99%

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Communication: Quantum mechanics without wavefunctions

Schiff

Poirier

2012

The Journal of Chemical Physics

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106

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We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications-theoretical, computational, and interpretational-are discussed.

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Section: Introductionmentioning

confidence: 88%

“…(9) (or any uniformizing choice of C), and writing x = ∂x/∂C,ẋ = ∂x/∂t etc., the PDE of Ref. 7 simplifies very substantially to…”

Section: The 1d Time-dependent Casementioning

confidence: 99%

Section: The 1d Time-independent Casementioning

confidence: 99%

“…(4)] and (scattering) TIQM states. 7 Any fourth-order ODE can be rewritten as a set of four coupled, first-order ODE's. Remarkably, Eq.…”

Section: The 1d Time-independent Casementioning

confidence: 99%

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Communication: Quantum mechanics without wavefunctions

Schiff

Poirier

2012

The Journal of Chemical Physics

Self Cite

106

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“…[58,59] When no information about the spectrum is known, pairs of eigenvalues and eigenfunctions of Eq. as an ODE, where the eigenvalues are treated as parameters.…”

Section: Numerical Methods For the Time-independent Integration Of Thmentioning

confidence: 99%

Deep nuclear resonant tunneling thermal rate constant calculations

Mandrà

Valleau

Ceotto

2013

Int J of Quantum Chemistry

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A fast and robust time‐independent method to calculate thermal rate constants in the deep resonant tunneling regime for scattering reactions is presented. The method is based on the calculation of the cumulative reaction probability which, once integrated, gives the thermal rate constant. We tested our method with both continuous (single and double Eckart barriers) and discontinuous first derivative potentials (single and double rectangular barriers). Our results show that the presented method is robust enough to deal with extreme resonating conditions such as multiple barrier potentials. Finally, the calculation of the thermal rate constant for double Eckart potentials with several quasi‐bound states and the comparison with the time‐independent log‐derivative method are reported. An implementation of the method using the Mathematica Suite is included in the Supporting Information. © 2013 Wiley Periodicals, Inc.

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