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1.
For a relativistic particle under a constant force and a linear velocity dissipation force, a constant of motion is found. Problems are shown for getting the Hamiltonian of this system. Thus, the quantization of this system is carried out through the constant of motion and using the quantization on the velocity variable. The dissipative relativistic quantum bouncer is outlined within this quantization approach.
PACS: 03.30.+p, 03.65.−w, 45.05.+x, 45.20Jj 相似文献
2.
For a one-dimensional dissipative system with position depending coefficient, two constant of motion are deduce. These constants
of motion bring about two Hamiltonians to describe the dynamics of same classical system. However, their quantization describe
the dynamics of two completely different quantum systems.
PACS numbers: 03.20.+i; 03.30.+ p; 03.65.-w 相似文献
3.
Gabriel González 《International Journal of Theoretical Physics》2007,46(3):417-423
A general formalism for obtaining the Lagrangian and Hamiltonian for a one-dimensional dissipative system is developed. The
formalism is illustrated by applying it to the case of a relativistic particle with linear dissipation. The relativistic wave
equation is solved for a free particle with linear dissipation.
PACS Numbers: 45.20.Jj, 03.65.Pm 相似文献
4.
G. López 《International Journal of Theoretical Physics》2001,40(10):1799-1807
A restricted constant of motion, Lagrangian and Hamiltonian, for the harmonic oscillator with quadratic dissipation is deduced. The restriction comes from the consideration of the constant of motion for the velocity of the particle either for v 0 or for v < 0. A study is done about the implications that these restricted variables have on the specific heat of a thermodynamical system of oscillators with this dissipation, and on the quantization of this dissipative system. 相似文献
5.
P.R. Giri 《The European Physical Journal C - Particles and Fields》2008,56(1):147-151
We show that the classical scale symmetry of a particle moving in string defect background is broken due to inequivalent quantization
of the classical system, which leads to scaling anomaly. The consequence of this anomaly is the formation of single bound
state in the coupling constant interval γ∈(-1,1). The inequivalent quantization is characterized by a 1-parameter family of
self-adjoint extension parameter ω.It has been conjectured that the formation of loosely bound state in string defect background
may lead to the so called anomalous scattering cross section for the particles, which has been experimentally observed in
molecular physics. A plausible laboratory test for the anomalous scattering could be devised in condensed matter system.
PACS 03.65.-w; 03.65.Db; 98.80.Cq; 11.27.+d 相似文献
6.
M Merad 《International Journal of Theoretical Physics》2007,46(8):2105-2118
The Duffin-Kemmer-Petiau (DKP) equation for spin 0 and 1 with smooth potential and position dependent- mass is solved. The
solution is given in terms of the Heun function. The step case for potential and mass are deduced as a limiting case. The
boundary conditions are also discussed.
PACS Numbers:03.30.+p, 03.65.Pm, 03.65.Ge, 03.65.Db 相似文献
7.
G. López 《International Journal of Theoretical Physics》2007,46(4):806-816
The Lagrangian, the Hamiltonian and the constant of motion of the gravitational attraction of two bodies when one of them
has variable mass is considered. The relative and center of mass coordinates are not separated, and choosing the reference
system in the body with much higher mass, it is possible to reduce the system of equations to 1-D problem. Then, a constant
of motion, the Lagrangian, and the Hamiltonian are obtained. The trajectories found in the space position-velocity,(x,v), are qualitatively different from those on the space position-momentum,(x,p).
PACS numbers: 03.20.+i 相似文献
8.
A. Lavagno A.M. Scarfone P. Narayana Swamy 《The European Physical Journal C - Particles and Fields》2006,47(1):253-261
On the basis of non-commutative q-calculus, we investigate a q-deformation of the classical Poisson bracket in order to formulate
a generalized q-deformed dynamics in the classical regime. The obtained q-deformed Poisson bracket appears invariant under
the action of the q-symplectic group of transformations. Within this framework we introduce the q-deformed Hamilton equations
and we derive the evolution equation for some simple q-deformed mechanical systems governed by a scalar potential dependent
only on the coordinate variable. It appears that the q-deformed Hamiltonian, which is the generator of the equation of motion,
is generally not conserved in time but, in correspondence, a new constant of motion is generated. Finally, by following the
standard canonical quantization rule, we compare the well-known q-deformed Heisenberg algebra with the algebra generated by
the q-deformed Poisson bracket.
PACS 02.45.Gh, 45.20.-d, 03.65.-w, 02.20.Uw 相似文献
9.
Using a suitable Laguerre basis set that ensures a tridiagonal matrix representation of the reference Hamiltonian, we were able to evaluate in closed form the matrix representation of the associated Hamiltonian for two exactly solvable 2D potentials. This enabled us to treat analytically the full Hamiltonian and compute the associated bound states spectrum as the eigenvalues of the associated analytical matrix representing their Hamiltonians. Finally we compared our results satisfactorily with those obtained using the Gauss quadrature numerical integration approach. PACS numbers: 03.65.Ge, 34.20.Cf, 03.65.Nk, 34.20.Gj 相似文献
10.
Omar Mustafa S. Habib Mazharimousavi 《International Journal of Theoretical Physics》2007,46(7):1786-1796
Ordering ambiguity associated with the von Roos position dependent mass (PDM) Hamiltonian is considered. An affine locally
scaled first order differential introduced, in Eq. (9), as a PDM-pseudo-momentum operator. Upon intertwining our Hamiltonian,
which is the sum of the square of this operator and the potential function, with the von Roos d-dimensional PDM-Hamiltonian, we observed that the so-called von Roos ambiguity parameters are strictly determined, but not
necessarily unique. Our new ambiguity parameters’ setting is subjected to Dutra’s and Almeida’s, Phys. Lett. A.
275 (2000) 25 reliability test and classified as good ordering.
PACS numbers: 03.65.Ge, 03.65. Fd, 03.65.Ca 相似文献
11.
Xing-Lei Xu Hong-Qi Li Ji-Suo Wang 《International Journal of Theoretical Physics》2006,45(12):2471-2482
Mesoscopic damped double resonance mutual capacitance coupled RLC circuit is quantized by the method of damped harmonic oscillator quantization. The Hamiltonian is diagonalized by unitary transformation. The eigenenergy spectra of this circuit are given. The quantum fluctuations of the charges and current of each loop are researched in excitation state of the squeezed vacuum state, the squeezed vacuum state and in vacuum state. It is show that, the quantum fluctuations of the charges and current are related to not only circuit inherent parameter and coupled magnitude, but also quantum number of excitation, squeezed coefficients, squeezed angle and damped resistance. And, because of damped resistance, the quantum fluctuation decay along with time.
PACS numbers: 03.65.-w,42.50.Lc. 相似文献
12.
M. Maamache S. Menouar L. Krache 《International Journal of Theoretical Physics》2006,45(11):2191-2198
By using the Lewis-Riesenfeld theory and algebraic method, we present an alternative approach to obtain the exact solution of time-dependent Hamiltonian systems involving quadratic, inverse quadratic and (1/x)p+p(1/x) terms. This solution is discussed and compared with that obtained by Choi, J. R. (2003). International Journal of Theoretical Physics
42, 853].
PACS: 03.65Ge; 03.65Fd; 03.65Bz 相似文献
13.
A quantum dynamical treatment of the S-G effect, to the leading order in
for the electron, where
is the fine-structure constant, and for spin 1/2 charged particles (e.g., the proton), in general, leads to a unitary expression for the probability density on the observation screen, where the magnetic field has a controllable longitudinal uniform component along the initial average direction of propagation of the particle, in addition to a non-uniform, almost longitudinal, magnetic field lying in the plane defined by the quantization axis, in question, of the spin and the initial average direction of propagation.Received: 3 April 2003, Published online: 22 July 2003PACS:
03.65.-w Quantum mechanics - 03.65.Nk Scattering theory - 24.70.+s Polarization phenomena in reactions 相似文献
14.
In analogy with the fact that there are magnetic moments associated respectively with the electron's orbital and spin motion in an atom we present several analyses on a proposal to introduce a concept of intrinsic magnetic flux associated with the electron's orbital and spin motion. It would be interesting to test or to demonstrate Faraday's and Lenz's laws of electromagnetic induction arising directly from the flux change due to transition of states in an atom and to examine applications of this concept of intrinsic flux.
PACS: 03.65.-w, 03.65.Ca, 03.65.Ta. 相似文献
15.
Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized
SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the
system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent
phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are
studied. We applied our result to the Caldirola–Kanai oscillator. The probability density of these coherent states for the
Caldirola–Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state
probability densities for the driven system are somewhat deformed.
PACS Numbers: 02.20.Sv, 03.65.-w, 03.65.Fd 相似文献
16.
Rajesh R. Parwani 《International Journal of Theoretical Physics》2006,45(10):1901-1913
The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular its linearity, in intuitive terms. Furthermore it allows for a physically motivated and systematic investigation of potential generalisations which are briefly discussed.
Pacs: 03.65.-w; 04.20.-q; 03.30.+ p; 11.10. Lm 相似文献
17.
The projective Hilbert space carries a natural symplectic structure which enables one to reformulate quantum dynamics as a
classical Hamiltonian one.
PACS: 03.65.Ta, 02.40.Yy, 45.20.Jj. 相似文献
18.
H. Nikolić 《The European Physical Journal C - Particles and Fields》2006,47(2):525-529
The covariant canonical method of quantization based on the De Donder–Weyl covariant canonical formalism is used to formulate
a world-sheet covariant quantization of bosonic strings. To provide the consistency with the standard non-covariant canonical
quantization, it is necessary to adopt a Bohmian deterministic hidden-variable equation of motion. In this way, string theory
suggests a solution to the problem of measurement in quantum mechanics.
PACS 11.25.-w; 04.60.Ds; 03.65.Ta 相似文献
19.
F. Bagarello 《International Journal of Theoretical Physics》2005,44(8):1193-1216
We adapt ideas coming from Quantum Mechanics to develop a non-commutative strategy for the analysis of some systems of ordinary
differential equations. We show that the solution of such a system can be described by an unbounded, self-adjoint and densely
defined operator H which we call, in analogy with Quantum Mechanics, the Hamiltonian of the system.
We discuss the role of H in the analysis of the integrals of motion of the system. Finally, we apply this approach to several examples.
Pacs Numbers: 02.30.Hq, 03.65.-w, 03.65.Db 相似文献