Stark Energy Levels of Symmetric-Top Molecules

Shirley, J.H.

doi:10.1063/1.1733618

Cited by 49 publications

(5 citation statements)

References 8 publications

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“…The rotational Stark effect in a symmetric-top molecule is commonly studied by means of the model Hamiltonian [27][28][29]…”

Section: Polar Symmetric Top In a Uniform Electric Fieldmentioning

confidence: 99%

Exceptional points of the eigenvalues of parameter-dependent Hamiltonian operators

Amore¹,

Fernández²

2019

Preprint

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We calculate the exceptional points of the eigenvalues of several parameter-dependent Hamiltonian operators of mathematical and physical interest.We show that the calculation is greatly facilitated by the application of the discriminant to the secular determinant. In this way the problem reduces to finding the roots of a polynomial function of just one variable, the parameter in the Hamiltonian operator. As illustrative examples we consider a particle in a one-dimensional box with a polynomial potential, the periodic Mathieu equation, the Stark effect in a polar rigid rotor and in a polar symmetric top.

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“…The rotational Stark effect in a symmetric-top molecule is commonly studied by means of the model Hamiltonian [27][28][29]…”

Section: Polar Symmetric Top In a Uniform Electric Fieldmentioning

confidence: 99%

Exceptional points of the eigenvalues of parameter-dependent Hamiltonian operators

Amore¹,

Fernández²

2019

Preprint

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“…A symmetric top molecule in an electric field is an analogue of the Lagrange top. The Stark energy levels of symmetric top molecules were calculated by Shirley [6], and have been well studied in chemical physics. In the case of Lagrange top, M and K are conserved quantities and the eigenfunction is expressed by the superposition of D-functions with different J-values.…”

Section: Introductionmentioning

confidence: 99%

Kowalevski top in quantum mechanics

Matsuyama

2013

Annals of Physics

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The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant torus. Some of these spectra are nearly degenerate due to the multiplicity of the invariant torus. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra.

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“…Kusch & Hugh published a large table (although with fewer digits), including also values of j equal to 3 and 4 and higher field strengths. Shirley (1963) used the method of continued fractions for calculating the energy levels of rigid symmetric-top molecules, but the paper contains also numerical results concerning the rigid diatomic dipole molecule. Thomson & Dalby (1968) solved the continued fraction equation numerically by a computer and fitted to the results polynomials containing even powers (up to the tenth power) of the field strength parameter by a least-mean-square procedure.…”

Section: Introductionmentioning

confidence: 99%

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

Fröman

Larsson

1994

Phil. Trans. R. Soc. Lond. A

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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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Stark Energy Levels of Symmetric-Top Molecules

Cited by 49 publications

References 8 publications

Exceptional points of the eigenvalues of parameter-dependent Hamiltonian operators

Exceptional points of the eigenvalues of parameter-dependent Hamiltonian operators

Kowalevski top in quantum mechanics

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

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