Hamiltonians

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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: 32.6 Hamiltonian Structure

§32.6 Hamiltonian Structure

… ►The Hamiltonian for ${\text{P}}_{\text{I}}$ is … ►The Hamiltonian for ${\text{P}}_{\text{II}}$ is … ►The Hamiltonian for ${\text{P}}_{\text{III}}^{\prime }$ (§32.2(iii)) is … ►

3: Bibliography Y

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$L$-squared discretizations of the continuum: Radial kinetic energy and the Coulomb Hamiltonian. Phys. Rev. A 11 (4), pp. 1144–1156.

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Referenced by:

§18.39(iv), §18.39(iv), §18.39(iv), §18.40(ii).

Encodings:

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4: 36.13 Kelvin’s Ship-Wave Pattern

… ►The wake is a caustic of the “rays” defined by the dispersion relation (“Hamiltonian”) giving the frequency $\omega$ as a function of wavevector $𝐤$: …

5: 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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External Links:

ISSN 0556-2791, Document, MathReview

Referenced by:

§32.16.

Encodings:

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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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External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§29.19(i).

Encodings:

BibTeX

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6: 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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External Links:

MathReview, ZentralBlatt

Referenced by:

§25.17.

Encodings:

BibTeX

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7: 18.39 Applications in the Physical Sciences

… ►The fundamental quantum Schrödinger operator, also called the Hamiltonian, $\mathscr{H}$, is a second order differential operator of the form …

8: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►The sum of the kinetic and potential energies give the quantum Hamiltonian, or energy operator; often also referred to as a Schrödinger operator. …