Rotation of a rigid diatomic dipole molecule in a homogeneous electric field - II. Energy levels when the field is zero, very weak or very strong

The energy quantization problem for a rigid diatomic electric dipole molecule in a homogeneous static electric field is considered. The field-free case is treated in some detail, since it is difficult to find a comprehensive treatment in the literature. For the limiting case of very weak fields the available results of conventional perturbation theory are presented in lucid form. For the limiting case of very strong fields an easily survey able perturbation calculation is performed.

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Rotation of a rigid diatomic dipole molecule in a homogeneous electric field: I. Schrödinger equation. Quantization conditions according to phase-integral method

Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences ◽

10.1098/rsta.1994.0036 ◽

1994 ◽

Vol 347 (1682) ◽

pp. 1-22 ◽

Cited By ~ 2

Keyword(s):

Field Strength ◽

Schrödinger Equation ◽

Electric Field ◽

Electric Field Strength ◽

Integral Method ◽

Schrodinger Equation ◽

Energy Levels ◽

Base Function ◽

Dipole Molecule ◽

Phase Integral

After a brief historical discussion of the energy quantization according to quantum mechanics of the rigid diatomic dipole molecule in a static electric field, the Schrödinger equation for that system is recalled. Previous attempts to obtain the energy levels clearly indicate that there is a need for a reliable method yielding very accurate eigenvalues for all values of the electric field strength. This is accomplished with the aid of new quantization conditions obtained by means of a phase-integral method involving a general phase-integral approximation of arbitrary order generated from an unspecified base function, which is chosen in two different ways such that, when the electric field strength is equal to zero, simple limiting forms of the quantization conditions give the exact values of the energy levels. The two choices of the base function are expected to be appropriate in the cases when the absolute value of the magnetic quantum number m is sufficiently large and sufficiently small respectively. For every value of m at least one of the two base functions should be useful.

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Rotation of a rigid diatomic dipole molecule in a homogeneous electric field IV. New phase-integral quantization conditions, very accurate for arbitary values of the magnetic quantum number, expressed in terms of complete elliptic integrals: survey of their accuracy

Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences ◽

10.1098/rsta.1994.0039 ◽

1994 ◽

Vol 347 (1682) ◽

pp. 65-81

Keyword(s):

Electric Field ◽

Quantum Number ◽

Energy Levels ◽

Elliptic Integrals ◽

Magnetic Quantum Number ◽

Homogeneous Electric Field ◽

Base Function ◽

Dipole Molecule ◽

Phase Integral ◽

Complete Elliptic Integrals

New quantization conditions for the energy levels of a rigid diatomic dipole molecule in a homogeneous electric field of arbitrary strength, obtained by means of a phaseintegral method involving phase-integral approximations of arbitrary order generated from two particular choices of the base function, are expressed in terms of complete elliptic integrals in the first, third and fifth order of the phase-integral approximation. Previous results, derived for one convenient choice of the parameter £0 in the base function, namely £0 = 1/2|m|, where m is the magnetic quantum number, are used, and new formulas are derived for the other convenient choice £0 = 0. The accuracy of the eigenvalues obtained from the quantization conditions is demonstrated in a number of diagrams.

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ENERGY LEVELS IN A SPHERICAL QUANTUM DOT WITH PARABOLIC CONFINEMENT UNDER APPLIED ELECTRIC FIELDS

Modern Physics Letters B ◽

10.1142/s0217984901001999 ◽

2001 ◽

Vol 15 (16) ◽

pp. 545-554 ◽

Cited By ~ 25

Author(s):

ECATERINA C. NICULESCU

Keyword(s):

Quantum Dot ◽

Electric Field ◽

Electric Fields ◽

Energy Levels ◽

Electric Field Effect ◽

Electric Field Effects ◽

Barrier Heights ◽

Spherical Quantum Dot ◽

Parabolic Confinement ◽

Weak Fields

Using a variational procedure, we have studied the electric field effect on the electronic states in a spherical GaAs – Ga 1-x Al x As quantum dot with parabolic confinement in the case of both finite and infinite barrier heights. For single-particle states of electrons and heavy holes a relative weak Stark shift at weak fields and a transition to a stronger shift at higher fields is found. Compared with a spherical quantum dot with a rectangular confinement potential, the parabolic quantum dot presents a greater restriction to the carriers. As a result, the confinement energy is larger, while the electric field effects on the energy levels are weaker. We conclude that a spherical quantum dot with a parabolic confinement may be significant for practical application.

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