An Interdisciplinary Journal

* 2010, Vol.13, No.4, pp.352-367*

Quantum-mechanical system - spin 1 particle in an external
Coulomb field is studied on the base of the matrix Duffin -
Kemmer - Petiau formalism with the use of the tetrad technique.
Separation of the variables is performed with the help of Wigner
functions ; *j* and *m* stand for quantum numbers
determining the square and
the third projection of the total
angular momentum of the vector particle. With the help of parity
operator, the radial 10-equation system is divided into two
subsystem of 4 and 6 equations that correspond to parity *P*=(-1)^{j+1} and *P*= (-1)^{j} respectively. The system of 4
equation is reduced to a second order differential equation which
coincides with that arising in the case of a scalar particle in a
Coulomb potential. It is shown that the 6-equation system reduces
to two different second order differential equations for a "main"
function. One main equation reduces to a confluent
Heun equation and provides us with the energy spectrum. Another
main equation is a more complex one, and solutions for it remain
unknown.

*Key words: *
quantum mechanics, spin 1 particle, bound states,
Coulomb field

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Last updated: *March 10, 2011*