Geodesic
Connection between Cartesian and polar wave functions of a~nonrelativistic charged particle in a~homogeneous magnetic field
Teoretičeskaâ i matematičeskaâ fizika, Tome 40 (1979) no. 1, pp. 140-143

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A linear transformation is found between the Cartesian and polar wave functions of a nonrelativistic charged particle moving in a homogeneous magnetic field. It is shown that the coefficients of this linear transformation coincide with the normalized Hermite functions $\overline H_n(y_0/a)$, where $y_0=a^2p_x/\hbar$, $p_x$ is the projection of the momentum, and $a$ is a parameter with the dimensions of a length characteristic of the investigated problem. 
@article{TMF_1979_40_1_a14,
     author = {G. S. Pogosyan and V. M. Ter-Antonyan},
     title = {Connection between {Cartesian} and polar wave functions of a~nonrelativistic charged particle in a~homogeneous magnetic field},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {140--143},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1979_40_1_a14/}
}
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G. S. Pogosyan; V. M. Ter-Antonyan. Connection between Cartesian and polar wave functions of a~nonrelativistic charged particle in a~homogeneous magnetic field. Teoretičeskaâ i matematičeskaâ fizika, Tome 40 (1979) no. 1, pp. 140-143. http://geodesic.mathdoc.fr/item/TMF_1979_40_1_a14/