相关论文: The variational method applied to the harmonic osc…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
The single well 1D harmonic oscillator is one of the most fundamental and commonly solved problems in quantum mechanics. Traditionally, in most introductory quantum mechanics textbooks, it is solved using either a power series method, which…
The quantum quartic anharmonic oscillator with the Hamiltonian $H=\frac{1}{2}\left( p^{2}+x^{2}\right) +\lambda x^{4}$ is a classical and fundamental model that plays a key role in various branches of physics, including quantum mechanics,…
We consider a particular discretization of the harmonic oscillator which admits an orthogonal basis of eigenfunctions called Kravchuk functions possessing appealing properties from the numerical point of view. We analytically prove the…
Within the approach of Supersymmetric Quantum Mechanics associated with the variational method a recipe to construct the superpotential of three dimensional confined potentials in general is proposed. To illustrate the construction, the…
In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitean matrices is…
We investigate the one-dimensional Schr\"{o}dinger equation for a harmonic oscillator with a finite jump $a$ at the origin. The solution is constructed by employing the ordinary matching-of-wavefunctions technique. For the special choices…
We describe a method for the calculation of accurate energy eigenvalues and expectation values of observables of separable quantum-mechanical models. We discuss the application of the approach to one-dimensional anharmonic oscillators with…
In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as…
We systematically investigate different versions of variational perturbation theory by forcing not only the first or second but also higher derivatives of the approximant with respect to the variational parameter to vanish. The choice of…
The variational perturbation theory for wave functions, which has been shown to work well for bound states of the anharmonic oscillator, is applied to resonance states of the anharmonic oscillator with negative coupling constant. We obtain…
We show that this problem gives rise to the same differential equation of a well known potential of ordinary quantum mechanics. However there is a subtle difference in the choice of the parameters of the hypergeometric function solving the…
We make use of a recently developed method to, not only obtain the exactly known eigenstates and eigenvalues of a number of quasi-exactly solvable Hamiltonians, but also construct a convergent approximation scheme for locating those levels,…
We introduce various optimization schemes for highly accurate calculation of the eigenvalues and the eigenfunctions of the one-dimensional anharmonic oscillators. We present several methods of analytically fixing the nonlinear variational…
With only a few exceptions, the numerical simulation of cosmic and laboratory hydromagnetic dynamos has been carried out in the framework of the differential equation method. However, the integral equation method is known to provide robust…
Using the technique of tridiagonal representation approach; for the first time, we extend this method to study quantum systems with literally perturbed Hamiltonians. Specifically, we consider a quantum system in a 3D spherical oscillator…
We consider three different approaches to analyze the quantum mechanical problems in multi-well potentials: i) the standard matrix diagonalization technique in the basis sets of harmonic oscillator eigenfunctions or plain waves; ii) the…
By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some…
The problem of bound states in delta potentials is revisited by means of Fourier transform approach. The problem in a simple delta potential sums up to solve an algebraic equation of degree one for the Fourier transform of the eigenfunction…
The formalism of Supersymmetric Quantum Mechanics provides us the eigenfunctions to be used in the variational mathod to obtain the eigenvalues for the Hulth\'en Potential.