Related papers: Eigenstates with the auxiliary field method
We propose a new method to obtain approximate solutions for the Schr\"{o}dinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical…
The auxiliary field method is a technique to obtain approximate closed formulae for the solutions of both nonrelativistic and semirelativistic eigenequations in quantum mechanics. For a many-body Hamiltonian describing identical particles,…
The auxiliary field method is a new technique to obtain closed formulae for the solutions of eigenequations in quantum mechanics. The idea is to replace a Hamiltonian $H$ for which analytical solutions are not known by another one $\tilde…
The auxiliary field method is a new and efficient way to compute approximate analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This method has already been successfully applied to the case of central potentials of…
It has recently been shown that the auxiliary field method is an interesting tool to compute approximate analytical solutions of the Schr\"{o}dinger equation. This technique can generate the spectrum associated with an arbitrary potential…
Using the auxiliary field method, we give an analytical expression for the eigenenergies of a system composed of two non-relativistic particles interacting via a potential of type $\sqrt{a^2 r^2 + b}$. This situation is usual in the case of…
Approximate analytical energy formulas for N-body relativistic Hamiltonians with one- and two-body interactions are obtained within the framework of the auxiliary field method. This method has already been proved to be a powerful technique…
Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form $\sigma\sqrt{\bm p^{2}+m^2}+V(r)$ are obtained within the framework of the auxiliary field method. This method, which is equivalent to the envelope…
The auxiliary field method has been recently proposed as an efficient technique to compute analytical approximate solutions of eigenequations in quantum mechanics. We show that the auxiliary field method is completely equivalent to the…
The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for $N$ identical particles in $D$ dimensions. The quality of the approximate eigenvalues can be improved…
We propose an approximate solution of the time-dependent Schr\"odinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of the…
Many-body forces are sometimes a relevant ingredient in various fields, such as atomic, nuclear or hadronic physics. Their precise structure is generally difficult to uncover. So, phenomenological effective forces are often used in…
The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…
We propose a quantum Monte Carlo approach to solve the ground state many-body Schrodinger equation for the electronic ground state. The method combines optimization from variational Monte Carlo and propagation from auxiliary field quantum…
The eigenenergies $\epsilon^{(N)}(m;\{n_i,l_i\})$ of a system of $N$ identical particles with a mass $m$ are functions of the various radial quantum numbers $n_i$ and orbital quantum numbers $l_i$. Approximations $E^{(N)}(m;Q)$ of these…
We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. It is shown that exact few-fermion eigenstates of the resulting Hamiltonian can be…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
The auxiliary field method, defined through introducing an auxiliary (also called as the Hubbard-Stratonovich or the Mean-) field and utilizing a loop-expansion, gives an excellent result for a wide range of a coupling constant. The…
Using closed positive extensions of the quadratic form in the potential term we provide alternative solutions to the eigenstate equation for the free quantum field Hamiltonian in the Schr\"o\-din\-ger representation. We show that admissible…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…