Hamiltonian systems

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1: 29.19 Physical Applications

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§29.19(i) Lamé Functions

… ►Brack et al. (2001) shows that Lamé functions occur at bifurcations in chaotic Hamiltonian systems. …

2: Bibliography B

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Integrable Hamiltonian systems and the Painlevé property. Phys. Rev. A (3) 25 (3), pp. 1257–1264.

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ISSN 0556-2791, Document, MathReview

Referenced by:

§32.16.

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Occurrence of periodic Lamé functions at bifurcations in chaotic Hamiltonian systems. J. Phys. A 34 (40), pp. 8199–8220.

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ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§29.19(i).

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3: 32.6 Hamiltonian Structure

… ► ${\text{P}}_{\text{I}}$–${\text{P}}_{\text{VI}}$ can be written as a Hamiltonian system …

4: Bibliography

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The Riemann Hypothesis and the Hamiltonian of a Quantum Mechanical System. In Number Theory and Dynamical Systems (York, 1987), M. M. Dodson and J. A. G. Vickers (Eds.), London Math. Soc. Lecture Note Ser., Vol. 134, pp. 153–172.

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MathReview, ZentralBlatt

Referenced by:

§25.17.

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5: 18.39 Applications in the Physical Sciences

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Introduction and One-Dimensional (1D) Systems

►The fundamental quantum Schrödinger operator, also called the Hamiltonian, $\mathscr{H}$, is a second order differential operator of the form … ►As in classical dynamics this sum is the total energy of the one particle system. … ►

1D Quantum Systems with Analytically Known Stationary States

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§18.39(ii) A 3D Separable Quantum System, the Hydrogen Atom

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