Exact solutions of a particle in a box with a delta function potential: The factorization method

Pedram, Pouria; Vahabi, Mohammad

doi:10.1119/1.3373925

Cited by 10 publications

(17 citation statements)

References 7 publications

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“…Since both V (L op ) ≫ ε N and V (L op ) ≪ ε N are two sources of error, we demanded that the proportionality coefficient α(k) to be of the order of one. For the trigonometric basis set, we suggested some ansatz for α(k) with the condition α(2) = 1 and found that L (2) op gives the most accurate results. By defining L S we showed that it can be also used as an accurate optimal length.…”

Section: Discussionmentioning

confidence: 99%

“…6, we depicted the coefficient of proportionality α(k) for the proposed schemes. Since α op grows exponentially, it cannot be used efficiently for large k. On the other hand, α S , α (1) op , and α (2) op go to π 2 /4 and α T goes to 2/3 at this limit.…”

Section: Stationarity Of the Trace Of The Hamiltonianmentioning

confidence: 99%

“…op gives the most accurate energy spectrum. As a simple application, in Table 2, we have reported the ground state energy of the anharmonic oscillators using only one basis function (N = 1) and the optimal length L (2) op . For these cases, the matrix of the Hamiltonian has only one element and the relative error is less than 20%.…”

Section: Alternative Proposalsmentioning

confidence: 99%

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Anharmonic oscillator and the optimized basis expansion

Pedram¹

2013

Applied Mathematics and Computation

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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 parameter specified by the domain of the trigonometric basis functions. We show that the optimized parameter enables us to determine the energy spectrum to an arbitrary accuracy. Also, using the harmonic oscillator basis functions, we indicate that the resulting optimal frequency agrees with the one obtained by the principle of the minimal sensitivity.Comment: 15 pages, 7 figures, to appear in Applied Mathematics and Computatio

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Section: Discussionmentioning

confidence: 99%

Section: Stationarity Of the Trace Of The Hamiltonianmentioning

confidence: 99%

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Anharmonic oscillator and the optimized basis expansion

Pedram¹

2013

Applied Mathematics and Computation

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“…for the confined system are well known (see, e.g., [27]) and can be separated into symmetric and antisymmetric solutions due to the symmetry of the problem. The latter are not affected by the δ-potential and coincide with the antisymmetric solutions of a particle in a box:…”

Section: One Particle In a δ-Potentialmentioning

confidence: 99%

Semiclassics in a system without classical limit: The few-body spectrum of two interacting bosons in one dimension

et al. 2017

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We present a semiclassical study of the spectrum of a few-body system consisting of two short-range interacting bosonic particles in one dimension, a particular case of a general class of integrable many-body systems where the energy spectrum is given by the solution of algebraic transcendental equations. By an exact mapping between δ-potentials and boundary conditions on the few-body wave functions, we are able to extend previous semiclassical results for single-particle systems with mixed boundary conditions to the two-body problem. The semiclassical approach allows us to derive explicit analytical results for the smooth part of the two-body density of states that are in excellent agreement with numerical calculations. It further enables us to include the effect of bound states in the attractive case. Remarkably, for the particular case of two particles in one dimension, the discrete energy levels obtained through a requantization condition of the smooth density of states are essentially in perfect agreement with the exact ones.

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“…In this work, we describe the isothermal expansion of the quantum Szilard engine by considering a quantum gas confined in a one-dimensional cylinder [11,12]. Although some previous studies, such as Refs.…”

Section: Introductionmentioning

confidence: 99%

Quantum isothermal reversible process of particles in a box with a delta potential

Park

Baek

2015

Journal of the Korean Physical Society

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For an understanding of a heat engine working in the microscopic scale, it is often necessary to estimate the amount of reversible work extracted by isothermal expansion of the quantum gas used as its working substance. We consider an engine with a movable wall, modeled as an infinite square well with a delta peak inside. By solving the resulting one-dimensional Schrödinger equation, we obtain the energy levels and the thermodynamic potentials. Our result shows how quantum tunneling degrades the engine by decreasing the amount of reversible work during the isothermal expansion.

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Exact solutions of a particle in a box with a delta function potential: The factorization method

Cited by 10 publications

References 7 publications

Anharmonic oscillator and the optimized basis expansion

Anharmonic oscillator and the optimized basis expansion

Semiclassics in a system without classical limit: The few-body spectrum of two interacting bosons in one dimension

Quantum isothermal reversible process of particles in a box with a delta potential

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