[x, p] = i{h_bar} ? | Zendy

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[x, p] = i{h_bar} ?

Author(s) -

Jau Tang

Publication year - 1996

Publication title -

osti oai (u.s. department of energy office of scientific and technical information)

Language(s) - English

Resource type - Reports

DOI - 10.2172/204188

Subject(s) - physics , hamiltonian (control theory) , bar (unit) , mathematical physics , antiparticle , lie algebra , omega , harmonic oscillator , quantum mechanics , mathematics , electron , meteorology , mathematical optimization , lepton

Heisenberg`s commutation relation for position x and momentum p, and its validity for relativistic harmonic oscillators are examined, using the techniques of Lie algebra and dual-bosonic representation of x, p and the Hamiltonian H. A modification with [x, p] =i{h_bar}({minus_plus} 1 + H/m{sub 0}c{sup 2}) is proposed for a particle and an antiparticle in a harmonic potential. For a 2 {times} 2 matrix representation for x, p and H operators, the quantized eigenenergy E is given by (E - m{sub 0}c{sup 2})/{h_bar}{omega} = 3/2, 5/2, 7/2, ..., where 1/2 is not allowed

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