A Nonlinear Approach for Quantum Mechanics

Attilio Maccari


This work represents a possible way to achieve the Einstein-de Broglie soliton-particle concept. The weakly nonlinear Klein-Gordon equation (nonlinear quantum mechanics) is investigated by the asymptotic perturbation (AP) method for a particle confined in a box. The quantization of the energy with a slight difference with respect to the standard (linear) quantum mechanics is obtained. Both relativistic and non-relativistic cases are considered and the transition frequencies are slightly different for the linear and nonlinear quantum mechanics. Experimental verification is needed to choose between the two theories.


Quantum mechanics; relativity;

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A. C. Newell, Solitons in Mathematics and Physics, SIAM, Philadelphia, (1985).

L. Lam (editor), Introduction to Nonlinear Physics, Springer, New York, (1997).

A. T. Filippov, The Versatile Soliton, Birkhauser, Boston, (2000).

A. Maccari, ‘The Kadomtsev-Petviashvili equation as a source of integrable model equation’, Journal of Mathematical Physics 37, 6207-6212, (1996).

A. Maccari, ‘A generalized Hirota equation in 2+1 dimensions’, Journal of Mathematical Physics 39, 6547-6551, (1998).

A. Maccari, ‘Modulated motion and infinite-period homoclinic bifurcation for parametrically excited Liénard systems’, International Journal of Non-Linear Mechanics 35, 239-262, (2000).

A. Maccari, ‘Non-resonant interacting waves for the nonlinear Klein-Gordon equation in three-dimensional space’, Physica D 135, 331-344, (2000).

A. Maccari, ‘Non-resonant interacting three-dimensional water waves’, Chaos, Solitons and Fractals 14, 105-116, (2002).

A. Maccari, ‘Interacting dromions for electron acoustic waves’, Chaos, Solitons and Fractals 15, 141-152, (2003).

L. de Broglie, The current interpretation of Wave Mechanics - A Critical Study, Elsevier, Amsterdam, (1964).

A. Chados, E. Hadjimichael, C. Tze (editors), Solitons in Nuclear ed Elementary Particle Physics, World Scientific, Singapore, (1993).

A. Maccari, ‘Approximate particle-like solutions for a nonlinear relativistic scalar complex field model in 3+1 dimensions’, Physics Letters A 276, 79-90, (2000).

A. Maccari, ‘Coherent solutions for relativistic vectorial fields’, Journal of Mathematical Physics 45, 4506-4514, (2004)

A. Maccari, ‘Chaos, solitons and fractals in the nonlinear Dirac equation’, Physics Letters A 336, 117-125, (2005).

A. Maccari, ‘Chaos, solitons and fractals in hidden symmetry models’, Chaos, Solitons and Fractals 27, 363-376, 2006


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