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Discrete and Continuous Quantum Mechanics, Exactly Solvable Models (Lessons in Quantum Intuition, Part II)
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| Soviet Journal of Particles and Nuclei |
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This review summarizes the series of investigations in "quantum engineering" and is the continuation of an article published earlier [Soviet J. Part. Nucle. 21, 384 (1990)]. "Quantum pictures" are presented which explain the features of wave motion over lattices (of channels and configurations). These allow a qualitatively new view of the structure of bound states and scattering mechanism: they tell what interaction is necessary to generate the desired spectrum or resonance features. Unexpected manifestations of an invisible upper energy boundary of the allowed band in the discrete representation of the wave function (e.g., wave confinement on a potential slope) are demonstrated. The significance of "higher-order" (order >= 4) Schrödinger equations and new exactly solvable models are discussed. This provides a bridge between nuclear (atomic) physics and solid-state quantum physics.
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