Quantum harmonic oscillator with time-dependent mass and frequency

Ding, Shangwu; Khan, Raphaël; Jialun, Zhang; Shen, Wei-Dong

doi:10.1007/bf00671596

Cited by 14 publications

(15 citation statements)

References 21 publications

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“…This boundary condition imposes the restriction that the number operator Ni for a particular type of i-universes has to be an invariant operator 5 . We can then follow the theory of invariants developed by Lewis [43] and others [44,45,46,47,48,49,50], and find a Hermitian invariant operator, Îi = h( b † i bi + 1 2 ), where [43] bi (a) ≡ 1 2h…”

Section: Boundary Conditions Of the Multiversementioning

confidence: 99%

Inter-universal entanglement

Robles-Pérez

2012

Preprint

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Section: Boundary Conditions Of the Multiversementioning

confidence: 99%

Inter-universal entanglement

Robles-Pérez

2012

Preprint

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“…We can then follow the theory of invariants developed by Lewis [43] and others [11,41,55,57,67,69,76], and find a Hermitian invariant operator,…”

Section: Boundary Conditions Of the Multiversementioning

confidence: 99%

Inter-Universal Entanglement

Robles-Pérez¹

2012

Open Questions in Cosmology

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“…where the function ψ n (t, x n ) is the wave function of a harmonic oscillator with timedependent mass and frequency, which can be written in terms of the wave function of a harmonic oscillator with constant mass and frequency [31][32][33][34]. The general solution of ψ n (t, x n ) can then be expanded in the basis of number eigenstates of the invariant representation, ψ N,n , as…”

Section: Small Perturbations and Backreactionmentioning

confidence: 99%

Quantum Cosmology with Third Quantisation

Robles-Pérez

2021

Universe

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We reviewed the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analysed the information contained in the solutions of the Wheeler–DeWitt equation and showed their interpretation in terms of the customary boundary conditions that are typically imposed on the semiclassical wave functions. In particular, we reviewed three different paradigms for the quantum creation of a homogeneous and isotropic universe. For the quantisation of a non-simply connected manifold, the best framework is the third quantisation formalism, in which the wave function of the universe is seen as a field that propagates in the space of Riemannian 3-geometries, which turns out to be isomorphic to a (part of a) 1 + 5 Minkowski spacetime. Thus, the quantisation of the wave function follows the customary formalism of a quantum field theory. A general review of the formalism is given, and the creation of the universes is analysed, including their initial expansion and the appearance of matter after inflation. These features are presented in more detail in the case of a homogeneous and isotropic universe. The main conclusion in both cases is that the most natural way in which the universes should be created is in entangled universe–antiuniverse pairs.

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Quantum harmonic oscillator with time-dependent mass and frequency

Cited by 14 publications

References 21 publications

Inter-universal entanglement

Inter-universal entanglement

Inter-Universal Entanglement

Quantum Cosmology with Third Quantisation

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