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In this note we consider a one-dimensional quantum mechanical particle constrained by a parabolic well perturbed by a Gaussian potential. As the related Birman-Schwinger operator is trace class, the Fredholm determinant can be exploited in…

Quantum Physics · Physics 2021-04-15 Silvestro Fassari , Luis M. Nieto , Fabio Rinaldi

Within the framework of the quark model and the variational method, the bound states of four heavy quarks (tetraquarks) are investigated. The basis variational wave functions are chosen in the Gaussian form. The matrix elements of the…

High Energy Physics - Phenomenology · Physics 2025-08-19 A. V. Eskin , A. P. Martynenko , F. A. Martynenko

When the energy content of a resonant mode of a crystalline solid in thermodynamic equilibrium is directly measured, assuming that quantum effects can be neglected it coincides with temperature except for a proportionality factor. This is…

A unified approach is used to study vibrational properties of periodic systems with first-principles methods and including anharmonic effects. Our approach provides a theoretical basis for the determination of phonon-dependent quantities at…

Materials Science · Physics 2014-06-12 Bartomeu Monserrat , N. D. Drummond , R. J. Needs

The three dimensional harmonic oscillator model including a cranking term is used for an energy variational calculation. Energy minima are found under variation of the three oscillator frequencies determining the shape of the system for…

Nuclear Theory · Physics 2009-11-07 W. D. Heiss , R. G. Nazmitdinov

A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our…

Atomic Physics · Physics 2015-05-19 Alexei M Frolov , David M. Wardlaw

The Hubbard model is a challenging quantum many-body problem and serves as a benchmark for quantum computing research. Accurate computation of its ground and excited state energies is essential for understanding correlated electron systems.…

Quantum Physics · Physics 2025-09-03 Mrinal Dev , Bikash K. Behera , Vivek Vyas , Prasanta K. Panigrahi

We present an approximative calculation of the ground-state energy for the anisotropic anharmonic oscillator Using an instanton solution of the isotropic action $\delta = 0$, we obtain the imaginary part of the ground-state energy for small…

Quantum Physics · Physics 2009-10-30 H. Kleinert , S. Thoms

The statistical mechanics of 1D and 2D Ginzburg-Landau systems is evaluated analytically, via the transfer matrix method, using an expression of the ground state energy of the quartic anharmonic oscillator in an external field. In the 2D…

Statistical Mechanics · Physics 2009-12-16 Victor Barsan

We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in…

Mathematical Physics · Physics 2009-11-11 Nasser Saad , Richard L. Hall , Hakan Ciftci

The nonrelativistic energies of the homonuclear ion T$_2^+$ are calculated for the ground state using the Lagrange-mesh method as was done for the isotopomers H$_2^+$ and D$_2^+$ ({\it J. Phys. B: At. Mol. Opt. Phys.} {\bf 45} 065101 and…

Atomic and Molecular Clusters · Physics 2015-06-19 Horacio Olivares Pilón

Anharmonic oscillators with the sextic and decatic potentials are studied employing the refinable interpolating scale functions. This method yields highly accurate values of both energy eigenvalues and eigenfunctions for the sextic and…

Quantum Physics · Physics 2020-01-07 K. Manimegalai , Swaraj Paul , M. M. Panja , Tapas Sil

By use of the recently derived $universal$ discrete imaginary-time propagator of the harmonic oscillator, both thermodynamic and Hamiltonian energies can be given analytically, and evaluated numerically at each imaginary time step, for…

Quantum Physics · Physics 2024-07-01 Siu A. Chin

We analyze recent results for a harmonic oscillator in an environment with a pointlike defect. We show that the allowed oscillator frequencies predicted by the authors stem from a misinterpretation of the exact solutions of a conditionally…

Quantum Physics · Physics 2020-12-30 Francisco M. Fernández

The optimization of neural wave functions in variational Monte Carlo crucially relies on a robust convergence criterion. While the energy variance is theoretically a definitive measure, its practical application as a primary convergence…

Quantum Physics · Physics 2025-11-03 Huan-Chen Shi , Er-Liang Cui , Dan Zhou

The frequency of a classical periodic system and the energy levels of the corresponding quantum system can both be obtained using action variables. We demonstrate the construction of two forms of the action variable for a one dimensional…

Quantum Physics · Physics 2007-05-23 M. K. Balasubramanya

An electronically variational approach to the calculation of atomic hyperfine structure transition energies under the influence of static external electric fields is presented. The method avoids the calculation of intermediate atomic states…

Atomic Physics · Physics 2025-08-29 Timo Fleig

The inversion potential for the ammonia molecule is approximated by a quartic function. The Hamiltonian thereby contains only even powers of p and x and a representation in terms of ladder operators a and a^+ is suggested. The frequency…

Chemical Physics · Physics 2018-09-24 S M Blinder

For the variational quantum eigensolver we propose to generate trial wavefunctions from a small amount of selected Pauli terms of the problem Hamiltonian. Two different approaches, one inspired by the quantum approximate optimization…

Quantum Physics · Physics 2019-08-27 Gian Salis , Nikolaj Moll

We address quantum systems isospectral to the harmonic oscillator, as those found within the framework of supersymmetric quantum mechanics, as potential resources for continuous variable quantum information. These deformed oscillator…

Quantum Physics · Physics 2025-04-04 Abdelatif Chabane , Sidali Mohammdi , Abdelhakim Gharbi , Matteo G. A. Paris