Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    An uncertainty principle for fermions with generalized kinetic energy (1983)
    Springer
    Communications in mathematical physics 90 (1983), S. 511-520 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We derive semiclassical upper bounds for the number of bound states and the sum of negative eigenvalues of the one-particle Hamiltoniansh=f(−i∇)+V(x) acting onL 2(ℝn). These bounds are then used to derive a lower bound on the kinetic energy $$\sum\limits_{j = 1}^N {\left\langle {\psi ,f( - i\nabla _j )\psi } \right\rangle }$$ for anN-fermion wavefunction ψ. We discuss two examples in more detail:f(p)=|p| andf(p)=(p 2+m 2)1/2−m, both in three dimensions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01216182
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    One-electron relativistic molecules with Coulomb interaction (1983)
    Springer
    Communications in mathematical physics 90 (1983), S. 497-510 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract As an approximation to a relativistic one-electron molecule, we study the operator $$H = ( - \Delta + m^2 )^{1/2} - e^2 \sum\limits_{j = 1}^K {Z_j } |x - R_j |^{ - 1}$$ withZ j ≧0,e −2=137.04.H is bounded below if and only ife 2 Z j ≦2/π allj. Assuming this condition, the system is unstable whene 2∑Z j 〉2/π in the sense thatE 0=inf spec(H)→−∞ as the R j →0, allj. We prove that the nuclear Coulomb repulsion more than restores stability; namely $$E_0 + 0.069e^2 \sum\limits_{i〈 j} {Z_i Z_j } |R_i - R_j |^{ - 1} \geqq 0$$ . We also show thatE 0 is an increasing function of the internuclear distances |R i −R j |.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01216181
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    One electron molecules with relativistic kinetic energy: Properties of the discrete spectrum (1984)
    Springer
    Communications in mathematical physics 94 (1984), S. 523-535 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We discuss the discrete spectrum of the operator $$H_K (c) = \left[ { - \hbar ^2 c^2 \Delta + m^2 c^4 } \right]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - \sum\limits_{k = 1}^K {Z_k e^2 \left| {x - R_k } \right|^{ - 1} } $$ . More specifically, we study 1) the behaviour of the eigenvalues when the internuclear distances contract, 2) the existence of ac-independent lower bound forH K (c)−mc 2, 3) the nonrelativistic limit of the eigenvalues ofH K (c)−mc 2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01403885
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Wiener measures for path integrals with affine kinematic variables (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 85-102 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The results obtained earlier have been generalized to show that the path integral for the affine coherent state matrix element of a unitary evolution operator exp(−iTH) can be written as a well-defined Wiener integral, involving Wiener measure on the Lobachevsky half-plane, in the limit that the diffusion constant diverges. This approach works for a wide class of Hamiltonians, including, e.g., −d2/dx2+V(x) on L2(R+), with V sufficiently singular at x=0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527812
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Quantum-mechanical path integrals with Wiener measure for all polynomial Hamiltonians. II (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2239-2256 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The coherent-state representation of quantum-mechanical propagators as well-defined phase-space path integrals involving Wiener measure on continuous phase-space paths in the limit that the diffusion constant diverges is formulated and proved. This construction covers a wide class of self-adjoint Hamiltonians, including all those which are polynomials in the Heisenberg operators; in fact, this method also applies to maximal symmetric Hamiltonians that do not possess a self-adjoint extension. This construction also leads to a natural covariance of the path integral under canonical transformations. An entirely parallel discussion for spin variables leads to the representation of the propagator for an arbitrary spin-operator Hamiltonian as well-defined path integrals involving Wiener measure on the unit sphere, again in the limit that the diffusion constant diverges.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526803
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Painless nonorthogonal expansions (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 1271-1283 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In a Hilbert space H, discrete families of vectors {hj} with the property that f=∑j〈hj|| f〉hj for every f in H are considered. This expansion formula is obviously true if the family is an orthonormal basis of H, but also can hold in situations where the hj are not mutually orthogonal and are "overcomplete.'' The two classes of examples studied here are (i) appropriate sets of Weyl–Heisenberg coherent states, based on certain (non-Gaussian) fiducial vectors, and (ii) analogous families of affine coherent states. It is believed, that such "quasiorthogonal expansions'' will be a useful tool in many areas of theoretical physics and applied mathematics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527388
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    How does truncation of the mask affect a refinable function? (1995)
    Springer
    Constructive approximation 11 (1995), S. 365-380 
    Details
    ISSN: 1432-0940
    Keywords: 26A16 ; 26A18 ; 39B10 ; 40A30 ; Subdivision schemes ; Refinable functions ; Wavelets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract If the mask of a refinable function has infinitely many coefficients, or if the coefficients are irrational, then it is often replaced by a finite mask with coefficients with terminating decimal expansions when it comes to applications. This note studies how such truncation affects the refinable function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01208560
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    On the distributions corresponding to bounded operators in the Weyl quantization (1980)
    Springer
    Communications in mathematical physics 75 (1980), S. 229-238 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Using properties of an integral transform giving directly the matrix elements of a quantum mechanical operator from the corresponding classical function, we restrict the class of distributions corresponding to bounded operators. As a consequence, we can exhibit a class of functions yielding trace-class operators, and give a bound on their trace-norm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01212710
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    A characterization of subsystems in physics (1979)
    Springer
    Letters in mathematical physics 3 (1979), S. 11-17 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Working within the framework of the propositional system formalism, we use a previous study [1] of the description of two independent physical systems as one big physical system to derive a characterization of a (non-interacting) physical subsystem. We discuss the classical case and the quantum case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00959533
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    A mathematical condition for a sublattice of a propositional system to represent a physical subsystem, with a physical interpretation (1979)
    Springer
    Letters in mathematical physics 3 (1979), S. 19-27 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We display three equivalent conditions for a sublattice, isomorphic to aP $$(\tilde{H})$$ , of the propositional systemP(ℋ) of a quantum system to be the representation of a physical subsystem (see [1]). These conditions are valid for dim $$\tilde{H}$$ ⩾3. We prove that one of them is still necessary and sufficient if dim $$\tilde{H}$$ 〈3. A physical interpretation of this condition is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00959534
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...