Semi-classical quantization of the magnetic top

Arsenović, D.; Barut, A. O.; Marić, Z.; Božić, Mirjana

doi:10.1007/bf02741499

Cited by 13 publications

(26 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[27]- [37]. Their treatments either postulate the usual commutation rules for the Cartesian components of the spin operator in the non-rotating coordinate system, by analogy with the rules for orbital angular momentum, or postulate that the momenta conjugate to the Euler angles become operators equal to i −  times derivatives with respect to to the angles, by analogy with conjugate translational momenta.…”

Section: Nonrelativistic Rigid Rotatormentioning

confidence: 99%

Statistical Description of Nonrelativistic Classical Systems

Goedecke¹

2017

JMP

View full text Add to dashboard Cite

We prove that any nonrelativistic classical system must obey a statistical wave equation that is exactly the same as the Schrödinger equation for the system, including the usual "canonical quantization" and Hamiltonian operator, provided an unknown constant is set equal to  . We show why the two equations must have exactly the same sets of solutions, whereby this classical statistical theory (CST) and nonrelativistic quantum mechanics may differ only in their interpretations of the same quantitative results. We identify some of the different interpretations. We show that the results also imply nonrelativistic Lagrangian classical mechanics and the associated Newtonian laws of motion. We prove that the CST applied to a nonrelativistic rigid rotator yields spin angular momentum operators that obey the quantum commutation rules and allow both integer and half-odd-integer spin. We also note that the CST applied to systems of identical massive particles is mathematically equivalent to nonrelativistic quantum field theory for those particles.

show abstract

Section: Nonrelativistic Rigid Rotatormentioning

confidence: 99%

Statistical Description of Nonrelativistic Classical Systems

Goedecke¹

2017

JMP

View full text Add to dashboard Cite

show abstract

“…However, there are also some provisos and doubtful points here. The problem was noticed many years ago by W Pauli, J Reiss, and also by D Arsenović, AO Barut, M Božić, and Z Marič . Namely, there are situations when the configuration space Q is multiply connected and one can suspect that it is not wave function ψ but rather

\overset{ψ}{true} ψ

what is to be one‐valued.…”

Section: General Scheme Of the Schrödinger Wave Mechanicsmentioning

confidence: 99%

Quantized mechanics of affinely rigid bodies

Sławianowski

Kovalchuk

Gołubowska

et al. 2017

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we develop the main ideas of the quantized version of affinely rigid (homogeneously deformable) motion. We base our consideration on the usual Schrödinger formulation of quantum mechanics in the configuration manifold, which is given, in our case, by the affine group or equivalently by the semi-direct product of the linear group GL(n, R) and the space of translations R n , where n equals the dimension of the "physical space." In particular, we discuss the problem of dynamical invariance of the kinetic energy under the action of the whole affine group, not only under the isometry subgroup. Technically, the treatment is based on the 2-polar decomposition of the matrix of the internal configuration and on the Peter-Weyl theory of generalized Fourier series on Lie groups. One can hope that our results may be applied in quantum problems of elastic media and microstructured continua. KEYWORDS homogeneously deformable body, Peter-Weyl analysis, Schrödinger quantization 6900

show abstract

“…Their manifold will be denoted by Is(N, η; M, g) ⊂ AfI(N, M ). The isometry groups Is(N, η) ⊂ GAf(N ), Is(M, g) ⊂ GAf(M ) act on Is(N, η; M, g) respectively on the right and on the left in the sense of (2), (3). Obviously, in realistic classical mechanics of (metrically) rigid body mirror-reflected coordinates are excluded and the genuine configuration space is given by some connected component of Is(N, η; M, g).…”

Section: Classical Preliminariesmentioning

confidence: 99%

“…And just such situations are interesting in our model, where the configuration spaces of rigid and affinely-rigid bodies in dimensions n ≥ 3 have two-element homotopy groups. This point was stressed, e.g., in [2,3,4,5,43,46], where the possibility of doubly-valued wave functions for quantized rigid body was pointed out.…”

Section: General Ideas Of Quantizationmentioning

confidence: 99%

Quantization of Affine Bodies: Theory and Applications in Mechanics of Structured Media

Sławianowski

2007

Material Substructures in Complex Bodies

View full text Add to dashboard Cite

Discussed is kinematics and dynamics of bodies with affine degrees of freedom, i.e., homogeneously deformable "gyroscopes". The special stress is laid on the status and physical justification of affine dynamical invariance. On the basis of classical Hamiltonian formalism the Schroedinger quantization procedure is performed. Some methods of the partial separation of variables, analytical treatment and search of rigorous solutions are developed. The possiblity of applications in theory of structured media, nanophysics, and molecular physics is discussed.

show abstract

Semi-classical quantization of the magnetic top

Cited by 13 publications

References 5 publications

Statistical Description of Nonrelativistic Classical Systems

Statistical Description of Nonrelativistic Classical Systems

Quantized mechanics of affinely rigid bodies

Quantization of Affine Bodies: Theory and Applications in Mechanics of Structured Media

Contact Info

Product

Resources

About