Reality of the Wigner Functions and Quantization | Zendy

S. Nasiri | Zendy; Samira Bahrami | Zendy

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Reality of the Wigner Functions and Quantization

Author(s) -

S. Nasiri,

Samira Bahrami

Publication year - 2009

Publication title -

research letters in physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.136

H-Index - 13

eISSN - 1687-6903

pISSN - 1687-689X

DOI - 10.1155/2009/298790

Subject(s) - wigner distribution function , quantization (signal processing) , phase space , particle in a box , harmonic oscillator , action (physics) , lagrangian , classical mechanics , geometric quantization , quantum mechanics , mathematics , statistical mechanics , physics , quantum , mathematical physics , statistical physics , canonical quantization , quantum gravity , algorithm

Here we use the extended phase space formulation of quantum statistical mechanics proposed in an earlier work to define an extended lagrangian for Wigner's functions (WFs). The extended action defined by this lagrangian is a function of ordinary phase space variables. The reality condition of WFs is employed to quantize the extended action. The energy quantization is obtained as a direct consequence of the quantized action. The technique is applied to find the energy states of harmonic oscillator, particle in the box, and hydrogen atom as the illustrative examples

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