One-dimensional quasi-relativistic particle in the box

Details One-dimensional quasi-relativistic particle in the box One-dimensional quasi-relativistic particle in the box

2011-10-26

arxiv.org/abs/1110.5887v1

Physics

Mathematical Physics

43 pages, 5 figures; to be submitted soon, all comments welcome

Scientific paper

Two-term Weyl-type asymptotic law for the eigenvalues of one-dimensional quasi-relativistic Hamiltonian (-h^2 c^2 d^2/dx^2 + m^2 c^4)^(1/2) + V_well(x) (the Klein-Gordon square-root operator with electrostatic potential) with the infinite square well potential V_well(x) is given: the n-th eigenvalue is equal to (n pi/2 - pi/8) h c/a + O(1/n), where 2a is the width of the potential well. Simplicity of eigenvalues is proved. Some L^2 and L^infinity properties of eigenfunctions are also studied. Eigenvalues represent energies of a `massive particle in the box' quasi-relativistic model.

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