scholarly journals Heat equation on phase space and the classical limit of quantum mechanical expectation values

1976 ◽  
Vol 48 (3) ◽  
pp. 195-197 ◽  
Author(s):  
A. Grossmann ◽  
R. Seiler
Keyword(s):  
Phase Space ◽  
Heat Equation ◽  
Classical Limit ◽  
Quantum Mechanical ◽  
Expectation Values

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

Classical limit of fermions in phase space

2001 ◽  
Vol 42 (9) ◽  
pp. 4020-4030 ◽  
Author(s):  
A. O. Bolivar
Keyword(s):  
Phase Space ◽  
Classical Limit

scholarly journals Application of the quantum mechanical hypervirial theorems to even-power series potentials

2020 ◽  
Vol 5 ◽  
pp. 104
Author(s):  
T. E. Liolios ◽  
M. E. Grypeos
Keyword(s):  
Power Series ◽  
Excited States ◽  
Energy Operator ◽  
Quantum Mechanical ◽  
Expectation Values ◽  
Gaussian Potential ◽  
Energy Eigenvalues ◽  
The Mean ◽  
Potential Parameters ◽  
Feynman Theorem

The class of the even-power series potentials:V(r)=-D+ Σ_k^{\infty} V_kλ^kr^{2k+2}, Vo=ω^2>0, is studied with the aim of obtaining approximate analytic ex­pressions for the energy eigenvalues, the expectation values for the potential and the kinetic energy operator, and the mean square radii of the orbits of a particle in its ground and excited states. We use the Hypervirial Theorems (HVT) in conjunction with the Hellmann-Feynman Theorem (HFT) which provide a very powerful scheme especially for the treatment of that type of potentials, as previous studies have shown. The formalism is reviewed and the expressions of the above mentioned quantities are subsequently given in a convenient way in terms of the potential parameters and the mass of the particle, and are then applied to the case of the Gaussian potential and to the potential V(r)=-D/cosh^2(r/R). These expressions are given in the form of series expansions, the first terms of which yield in quite a number of cases values of very satisfactory accuracy.

scholarly journals Efficient classical computation of expectation values in a class of quantum circuits with an epistemically restricted phase space representation

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Agung Budiyono ◽  
Hermawan K. Dipojono
Keyword(s):  
Phase Space ◽  
Continuous Variable ◽  
Complex Hilbert Space ◽  
Quantum Circuits ◽  
Space Distribution ◽  
Space Representation ◽  
Specific Class ◽  
Expectation Values ◽  
Conceptual Tool ◽  
Quantum Uncertainty

Abstract We devise a classical algorithm which efficiently computes the quantum expectation values arising in a class of continuous variable quantum circuits wherein the final quantum observable—after the Heisenberg evolution associated with the circuits—is at most second order in momentum. The classical computational algorithm exploits a specific epistemic restriction in classical phase space which directly captures the quantum uncertainty relation, to transform the quantum circuits in the complex Hilbert space into classical albeit unconventional stochastic processes in the phase space. The resulting multidimensional integral is then evaluated using the Monte Carlo sampling method. The convergence rate of the classical sampling algorithm is determined by the variance of the classical physical quantity over the epistemically restricted phase space distribution. The work shows that for the specific class of computational schemes, Wigner negativity is not a sufficient resource for quantum speedup. It highlights the potential role of the epistemic restriction as an intuitive conceptual tool which may be used to study the boundary between quantum and classical computations.

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