Piezoelectric Properties of Triglycine Sulphate Crystal

Husimi, K.; Kataoka, Keita

doi:10.1143/jpsj.14.105

Cited by 105 publications

(127 citation statements)

References 1 publication

Supporting

Mentioning

111

Contrasting

Order By: Relevance

“…(24) and (25), with enough points to give at least 3-digit accuracy for Eq. (25). Values of ANI and NI reported in Table I were obtained by evaluating the integrals of Eqs.…”

Section: (9)mentioning

confidence: 87%

“…In such a formulation, the Wigner function would not be restricted to be nonnegative everywhere. Another approach would be to define the entropy in terms of the Husimi function that is nonnegative everywhere by its definition [25,26]. Here the constraints would be in terms of Gaussian convolutions of the density and kinetic energy density.…”

Section: If? Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Approximate density matrices and wigner distribution functions from density, kinetic energy density, and idempotency constraints

Morrison

Yang

Parr

et al. 1990

Int J of Quantum Chemistry

View full text Add to dashboard Cite

The Wigner distribution function and the corresponding density matrix are calculated using a form for the distribution function suggested by maximization of the entropy. Wigner functions and density matrices are determined by imposing conditions of idempotency on the density matrix. Exchange energies and Compton profiles calculated from density matrices obtained by imposing the idempotency constraints are compared with the results of calculations using the Hartree-Fock density matrix and a Gaussian approximation for the density matrix for H and the noble gases He through Xe. Compton profiles from Wigner functions with idempotency constraints show improvements over the Gaussian approximation for the lighter atoms, but do not show significant changes for the heavier atoms. Exchange energies from density matrices with idempotency constraints show improvements over the Gaussian approximation except for the heavier atoms Kr and Xe.

show abstract

“…(24) and (25), with enough points to give at least 3-digit accuracy for Eq. (25). Values of ANI and NI reported in Table I were obtained by evaluating the integrals of Eqs.…”

Section: (9)mentioning

confidence: 87%

Section: If? Discussionmentioning

confidence: 99%

Approximate density matrices and wigner distribution functions from density, kinetic energy density, and idempotency constraints

Morrison

Yang

Parr

et al. 1990

Int J of Quantum Chemistry

View full text Add to dashboard Cite

show abstract

“…Later Husimi [15] and Kano [16] introduced the function Q(q, p), which has only nonnegative values, but its continuous variables q and p are not physical observables (position and momentum), since the uncertainty relations [17,18,19] prohibit one from measuring simultaneously the position and momentum. This means that a joint probability distribution of two random continuous position and momentum does not exist.…”

Section: Introductionmentioning

confidence: 99%

Probability Representation of Quantum States as a Renaissance of Hidden Variables— God Plays Coins

Chernega¹,

Манько²,

Man’ko³

2019

J Russ Laser Res

View full text Add to dashboard Cite

We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -the states are identified with probability distributions and observables, with random variables. An example of the spin-1/2 state is considered. We show that the triada of Malevich's squares can be used to illustrate the qubit state. We formulate the superposition principle of quantum states in terms of probabilities determining the quantum states.New formulas for nonlinear addition rules of probabilities providing the probabilities associated with the interference of quantum states are obtained. The evolution equation for quantum states is given in the form of a kinetic equation for the probability distribution identified with the state.

show abstract

“…Continuing in the spirit of the approach by Moyal [5], Wigner [6], Husimi [7], et al, according to which quantum mechanics can be formulated in a natural manner in terms of functions on the classical phase space, recently [8] a different approach has been proposed dealing with probability distributions rather than quasi-probabilities of previous approaches. It is to be remarked that this approach differs from the one initiated by Koopman [9], who had shown how the dynamical transformations of classical mechanics considered as measure preserving transformations of the phase space, induce unitary transformations on the Hilbert space of functions which are square integrable with respect to a Liouville measure over the phase space.…”

Section: Introductionmentioning

confidence: 99%