共查询到20条相似文献,搜索用时 0 毫秒
1.
J. C. Fabris F. T. Falciano J. Marto N. Pinto-Neto P. Vargas Moniz 《Brazilian Journal of Physics》2012,42(5-6):475-481
A quantum cosmological model with radiation and a dilaton scalar field is analyzed. The Wheeler–DeWitt equation in the minisuperspace induces a Schrödinger equation, which can be solved. An explicit wavepacket is constructed for a particular choice of the ordering factor. A consistent solution is possible only when the scalar field is a phantom field. Moreover, although the wavepacket is time-dependent, a Bohmian analysis allows to extract a bouncing behavior for the scale factor. 相似文献
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Shi-Hai Dong 《International Journal of Theoretical Physics》2002,41(1):89-99
In this study the spectral problem of the two-dimensional Schrödinger equation with the cylindrically symmetrical decatic potential is carried out. The concept of quantum monodromy is introduced to give insight into the energy levels of system with this potential. It is shown that quantum monodromy occurs at = 0 in the distribution of eigenstates around a critical point on the spectrum at E = 0 with zero angular momentum, such that there can be no smoothly valid assignment of quantum number. Cases with the three-well and four-well potentials are presented to give rise to the double degeneracies with respect to energy except for the angular momentum m = 0. 相似文献
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D. Benedetto F. Castella R. Esposito M. Pulvirenti 《Communications in Mathematical Physics》2008,277(1):1-44
In this paper we analyze the asymptotic dynamics of a system of N quantum particles, in a weak coupling regime. Particles are assumed statistically independent at the initial time.
Our approach follows the strategy introduced by the authors in a previous work [BCEP1]: we compute the time evolution of the
Wigner transform of the one-particle reduced density matrix; it is represented by means of a perturbation series, whose expansion
is obtained upon iterating the Duhamel formula; this approach allows us to follow the arguments developed by Lanford [L] for
classical interacting particles evolving in a low density regime.
We prove, under suitable assumptions on the interaction potential, that the complete perturbation series converges term-by-term,
for all times, towards the solution of a Boltzmann equation.
The present paper completes the previous work [BCEP1]: it is proved there that a subseries of the complete perturbation expansion
converges uniformly, for short times, towards the solution to the nonlinear quantum Boltzmann equation. This previous result
holds for (smooth) potentials having possibly non-zero mean value. The present text establishes that the terms neglected at
once in [BCEP1], on a purely heuristic basis, indeed go term-by-term to zero along the weak coupling limit, at least for potentials
having zero mean.
Our analysis combines stationary phase arguments with considerations on the nature of the various Feynman graphs entering
the expansion. 相似文献
4.
Zhong-Qi Ma 《Foundations of Physics Letters》1999,12(6):561-570
The exact solution to the Schrödinger equation for the rigid body with the given angular momentum and parity is obtained. Since the quantum rigid body can be thought of as the simplest quantum three-body problem where the internal motion is frozen, this calculation method is a good starting point for solving the quantum three-body problems. 相似文献
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Jeffrey Rauch 《Communications in Mathematical Physics》1978,61(2):149-168
The main theorem asserts that ifH=+gV is a Schrödinger Hamiltonian with short rangeV, L
compact
2
(IR3), andR>0, then exp(iHt)
S
L
2
(|x|<R)=O(t
–1/2), ast where
S
is projection onto the orthogonal complement of the real eigenvectors ofH. For all but a discrete set ofg,O(t
–1/2) may be replaced byO(t
–3/2).Research supported by the National Science Foundation under grants NSF GP 34260 and MCS 72-05055 A04 相似文献
6.
Frank Hövermann Herbert Spohn Stefan Teufel 《Communications in Mathematical Physics》2001,215(3):609-629
We consider the dynamics generated by the Schr?dinger operator H=−?Δ+V(x)+W(ɛx), where V is a lattice periodic potential and W an external potential which varies slowly on the scale set by the lattice spacing. We prove that in the limit ɛ→ 0 the time
dependent position operator and, more generally, semiclassical observables converge strongly to a limit which is determined
by the semiclassical dynamics.
Received: 7 February 2000 / Accepted: 7 July 2000 相似文献
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Cevdet Tezcan Ramazan Sever Özlem Yeşiltaş 《International Journal of Theoretical Physics》2008,47(6):1713-1721
Effective mass Schrödinger equation is solved exactly for a given potential. Nikiforov-Uvarov method is used to obtain energy eigenvalues and the corresponding wave functions. A free parameter is used in the transformation of the wave function. The effective mass Schrödinger equation is also solved for the Morse potential transforming to the constant mass Schrödinger equation for a potential. One can also get solution of the effective mass Schrödinger equation starting from the constant mass Schrödinger equation. 相似文献
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Shi-Hai Dong 《International Journal of Theoretical Physics》2001,40(2):559-567
Applying an ansatz to the eigenfunction, we obtain the exact closed-form solutions of the relativistic Schrödinger equation with the potential V(r) = –a/r + b/r1/2 both in three dimensions and in two dimensions. The restrictions on the parameters of the given potential and the angular momentum quantum number are also presented. 相似文献
12.
M. D. Pollock 《Foundations of Physics》2014,44(4):368-388
The Schrödinger equation for a particle of rest mass $m$ and electrical charge $ne$ interacting with a four-vector potential $A_i$ can be derived as the non-relativistic limit of the Klein–Gordon equation $\left( \Box '+m^2\right) \varPsi =0$ for the wave function $\varPsi $ , where $\Box '=\eta ^{jk}\partial '_j\partial '_k$ and $\partial '_j=\partial _j -\mathrm {i}n e A_j$ , or equivalently from the one-dimensional action $S_1=-\int m ds +\int neA_i dx^i$ for the corresponding point particle in the semi-classical approximation $\varPsi \sim \exp {(\mathrm {i}S_1)}$ , both methods yielding the equation $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2m}\eta ^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + m + n e\phi \right) \varPsi $ in Minkowski space–time , where $\alpha ,\beta =1,2,3$ and $\phi =-A_0$ . We show that these two methods generally yield equations that differ in a curved background space–time $g_{ij}$ , although they coincide when $g_{0\alpha }=0$ if $m$ is replaced by the effective mass $\mathcal{M}\equiv \sqrt{m^2-\xi R}$ in both the Klein–Gordon action $S$ and $S_1$ , allowing for non-minimal coupling to the gravitational field, where $R$ is the Ricci scalar and $\xi $ is a constant. In this case $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2\mathcal{M}'} g^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + \mathcal{M}\phi ^{(\mathrm g)} + n e\phi \right) \varPsi $ , where $\phi ^{(\mathrm g)} =\sqrt{g_{00}}$ and $\mathcal{M}'=\mathcal{M}/\phi ^{(\mathrm g)} $ , the correctness of the gravitational contribution to the potential having been verified to linear order $m\phi ^{(\mathrm g)} $ in the thermal-neutron beam interferometry experiment due to Colella et al. Setting $n=2$ and regarding $\varPsi $ as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space–time. Conservation of probability and electrical current requires both electromagnetic gauge and space–time coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div ${{\varvec{A}}}=\hbox {div}{{\varvec{A}}}^{(\mathrm g)}=0$ , where ${{\varvec{A}}}^{\alpha }=-A^{\alpha }$ and ${{\varvec{A}}}^{(\mathrm g)\alpha }=-\phi ^{(\mathrm g)}g^{0\alpha }$ . The quantum-cosmological Schrödinger (Wheeler–DeWitt) equation is also discussed in the $\mathcal{D}$ -dimensional mini-superspace idealization, with particular regard to the vacuum potential $\mathcal V$ and the characteristics of the ground state, assuming a gravitational Lagrangian $L_\mathcal{D}$ which contains higher-derivative terms up to order $\mathcal{R}^4$ . For the heterotic superstring theory , $L_\mathcal{D}$ consists of an infinite series in $\alpha '\mathcal{R}$ , where $\alpha '$ is the Regge slope parameter, and in the perturbative approximation $\alpha '|\mathcal{R}| \ll 1$ , $\mathcal V$ is positive semi-definite for $\mathcal{D} \ge 4$ . The maximally symmetric ground state satisfying the field equations is Minkowski space for $3\le {\mathcal {D}}\le 7$ and anti-de Sitter space for $8 \le \mathcal {D} \le 10$ . 相似文献
13.
JETP Letters - The simulation of quantum systems on a quantum computer using the Zalka–Wiesner algorithm including quantum noise has been considered. The efficiency of developed methods and... 相似文献
14.
A. Dynin 《Russian Journal of Mathematical Physics》2014,21(2):169-188
Inspired by F. Wilczek’s QCD Lite, quantum Yang-Mills-Weyl Dynamics (YMWD) describes quantum interaction between gauge bosons (associated with a simple gauge group \(\mathbb{G}\) ) and larks (massless chiral fields charged by an irreducible unitary representation of \(\mathbb{G}\) ). Schrödinger representation of this quantum Yang-Mills-Weyl theory is based on a sesqui-holomorphic operator calculus of infinite-dimensional operators with variational derivatives. The spectrum of quantum YMWD in a compact bag is a sequence of eigenvalues convergent to +∞. The eigenvalues have finite multiplicities with respect to a von Neumann algebra with a regular trace. The spectrum is inversely proportional to the square of the running coupling constant. The rigorous mathematical theory is nonperturbative with a running coupling constant as the only ad hoc parameter. The application of the first mathematical principles is based on the properties of the compact simple Lie group \(\mathbb{G}\) . 相似文献
15.
Starting from the q-Heisenberg algebra, we derive from a few abstract principles a broad class of Schrödinger operators in lattice quantum mechanics for which one can determine explicit eigenvalues and spectral properties. This happens by algebras of creators and annihilators. Generalized inhomogeneous q-discrete Hermite polynomials occur via their recurrence relations. Within this framework we obtain the special case of an interesting result, proved by Christian Berg in a much larger ge-nerality: The orthogonality measure for q-discrete Hermite polynomials of type II is not uniquely determined on q-exponential lattices. 相似文献
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We discuss separability of solutions to a Schr?dinger equation that describes a composite quantum system and give some kinds of Hamiltonians H(t) such that the solution to Schr?dinger equation induced by H(t) is separable at any time provided that it is separable at t = 0. For example, we prove that if the Hamiltonian H is time-independent and equals to the product PA■PB of two projections on the subsystems KAand KB, respectively, then the state |ψ(t) of the composite system starting from a separable initial |ψ(0) = |ψA■|ψB is separable for all t ∈ [0, T] if and only if either |ψA is an eigenstate of PA, or |ψB is an eigenstate of PB. 相似文献
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Renato Pessoa Maurice de Koning Silvio Antonio Vitiello 《Journal of statistical physics》2009,134(4):769-780
We investigate the influence of anharmonic effects on the zero-point vacancy concentration in a boson system model in the
solid phase at T=0 K. We apply the reversible-work method to compute the vacancy formation free energy and the vacancy concentration in the
system. A comparison of our results with those obtained using the harmonic approximation show that anharmonic effects reduce
the formation free energy by ∼25%, leading to an increase of the zero-point vacancy concentration by more than an order of
magnitude. 相似文献