EVALUATION OF RELATIVISTIC TRANSITION MATRIX ELEMENTS OF HYDROGENIC ATOMS USING PLANE WAVE EXPANSION

For the first time to our knowledge, a general, explicit formula for exact transition matrix elements in relativistic hydrogenic atoms is derived, by using the plane-wave expansion for the electromagnetic-field vector potential. By applying the obtained formula, discrete-discrete and discrete-continuous matrix elements are evaluated analytically and numerically.

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CLOSED ANALYTIC FORM FOR EVALUATION OF RELATIVISTIC BOUND-UNBOUND AND UNBOUND-UNBOUND TRANSITION MATRIX ELEMENTS OF HYDROGENIC ATOMS

International Journal of Modern Physics B ◽

10.1142/s0217979208049364 ◽

2008 ◽

Vol 22 (29) ◽

pp. 5095-5102

Author(s):

A. V. SOLDATOV ◽

J. SEKE ◽

G. ADAM ◽

M. POLAK

Keyword(s):

Electromagnetic Field ◽

Plane Wave ◽

Vector Potential ◽

Transition Matrix ◽

Analytic Form ◽

Field Vector ◽

Matrix Elements ◽

Plane Wave Expansion ◽

Transition Matrix Elements ◽

Closed Analytic Form

A closed analytic form for relativistic bound-unbound and unbound-unbound transition matrix elements of hydrogenic atoms by using the plane-wave expansion for the electromagnetic-field vector potential is derived. By applying the obtained formulae, these transition matrix elements can be evaluated analytically and numerically.

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HYPERGEOMETRIC FUNCTION REPRESENTATION OF RELATIVISTIC TRANSITION MATRIX ELEMENTS FOR HYDROGENIC ATOMS

Modern Physics Letters B ◽

10.1142/s0217984909017881 ◽

2009 ◽

Vol 23 (02) ◽

pp. 111-119

Author(s):

A. V. SOLDATOV ◽

J. SEKE ◽

G. ADAM ◽

M. POLAK

Keyword(s):

Transition Matrix ◽

Numerical Evaluation ◽

Hypergeometric Functions ◽

Field Vector ◽

Matrix Elements ◽

Plane Wave Expansion ◽

Computationally Efficient ◽

The Matrix ◽

Transition Matrix Elements ◽

Computationally Efficient Algorithms

By using the plane-wave expansion for the electromagnetic-field vector potential, relativistic bound–bound, bound–unbound and unbound–unbound transition matrix elements for hydrogenic atoms are expressed universally in terms of hypergeometric functions. By applying the obtained formulas, these transition matrix elements can be evaluated analytically and numerically with arbitrarily high precision. The newfound representation for the matrix elements is very convenient for direct numerical evaluation of the Lamb shift because of its universality, conciseness and reliance on functions already built in the standard computational packages. All of this is highly favorable for programming of computationally efficient algorithms.

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Analytic evaluation of MOM matrix elements using the plane wave expansion

IEEE Antennas and Propagation Society International Symposium. Digest. Held in conjunction with: USNC/CNC/URSI North American Radio Sci. Meeting (Cat. No.03CH37450) ◽

10.1109/aps.2003.1219241 ◽

2004 ◽

Author(s):

M. Ayatollahi ◽

S. Safavi-Naeini

Keyword(s):

Plane Wave ◽

Matrix Elements ◽

Plane Wave Expansion ◽

Analytic Evaluation ◽

Wave Expansion

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OPTICAL TRANSITIONS IN A PARABOLIC GaAs/Ga1-xAlxAs SUPERLATTICES

Surface Review and Letters ◽

10.1142/s0218625x01001117 ◽

2001 ◽

Vol 08 (03n04) ◽

pp. 321-325

Author(s):

ŞAKIR ERKOÇ ◽

HATICE KÖKTEN

Keyword(s):

Transition Matrix ◽

Optical Transition ◽

Matrix Elements ◽

Electron States ◽

Parabolic Potential ◽

Consistent Field ◽

Self Consistent ◽

Self Consistent Field ◽

Transition Matrix Elements ◽

Scf Calculations

We have performed self-consistent field (SCF) calculations of the electronic structure of GaAs/Ga 1-x Al x As superlattices with parabolic potential profile within the effective mass theory. We have calculated the optical transition matrix elements involving transitions from the hole states to the electron states, and we have also computed the oscillator strength matrix elements for the transitions among the electron states.

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