aqora

Overview of Part IV

Lukas Burgholzer, Robert Wille

Springer eBooksJan 1, 20260 citations

Dynamics and excitations of Bose-Einstein condensates

J.-P. Martikainen

iii List of publications iv Summary of the original publications v Contribution by the author vi

Työväentutkimus VuosikirjaDec 1, 20013 citations

Summary of Part I

Alexander A. Lisyansky, E. S. Andrianov, Alexey P. Vinogradov +1 more

Springer series in optical sciences/SPringer series in optical sciencesJan 1, 20240 citations

Summary of Part III

Lukas Burgholzer, Robert Wille

Springer eBooksJan 1, 20260 citations

Physical (A)Causality: Determinism, Randomness and Uncaused Events

Karl Svozil

Part I Embedded observers, reflexive perception and representation: Intrinsic and extrinsic observation mode -- Embedded observers and self-expression -- Reflexive measurement -- Intrinsic self-representation -- Part II Provable unknowns: On what is entirely hopeless -- Forecasting and unpredictability -- Induction by rule inference -- Other types of recursion theoretic unknowables -- What if there are no laws? Emergence of laws -- Part III Quantum unknowns: "Shut up and calculate" -- Evolution by permutation -- Quantum mechanics in a nutshell -- Quantum oracles -- Vacuum fluctuations -- Radioactive decay -- Part IV Exotic unknowns: Classical continua and infinities -- Classical (in)determinism -- Deterministic chaos -- Partition logics, finite automata and generalized urn models -- Part V Transcendence: Miracles -- Dualistic interfaces -- Part VI Executive summary: Executive summary -- Appendix A: Formal (in)computability and randomness -- B: Two particle correlations and expectationsPart I Embedded observers, reflexive perception and representation: Intrinsic and extrinsic observation mode -- Embedded observers and self-expression -- Reflexive measurement -- Intrinsic self-representation -- Part II Provable unknowns: On what is entirely hopeless -- Forecasting and unpredictability -- Induction by rule inference -- Other types of recursion theoretic unknowables -- What if there are no laws? Emergence of laws -- Part III Quantum unknowns: "Shut up and calculate" -- Evolution by permutation -- Quantum mechanics in a nutshell -- Quantum oracles -- Vacuum fluctuations -- Radioactive decay -- Part IV Exotic unknowns: Classical continua and infinities -- Classical (in)determinism -- Deterministic chaos -- Partition logics, finite automata and generalized urn models -- Part V Transcendence: Miracles -- Dualistic interfaces -- Part VI Executive summary: Executive summary -- Appendix A: Formal (in)computability and randomness -- B: Two particle correlations and expectations

Feb 14, 201816 citations

IV.—On an Elementary Solution of a Partial Differential Equation of Parabolic Type. Part I

E. T. Copson

Summary Professor E. T. Whittaker has recently discovered a Third Quantum-Mechanical Principal Function R(q, Q, t - T) and has worked out the theory of this function in detail when the Hamiltonian is By using the Sturm-Liouville theory of linear differential equations and the properties of Green's function, it is shown that the function is an elementary solution of the adjoint of the Schrodinger wave equation associated with the Hamiltonian H. It is pointed out that the modified Planck constant ħ arises solely from the commutation relation and may, from the analytical view-point, be any constant, real or complex. In particular, if ħ = i, the use of an algebra with the commutation relation leads to an elementary solution of the real equation of parabolic typeSummary Professor E. T. Whittaker has recently discovered a Third Quantum-Mechanical Principal Function R(q, Q, t - T) and has worked out the theory of this function in detail when the Hamiltonian is By using the Sturm-Liouville theory of linear differential equations and the properties of Green's function, it is shown that the function is an elementary solution of the adjoint of the Schrodinger wave equation associated with the Hamiltonian H. It is pointed out that the modified Planck constant ħ arises solely from the commutation relation and may, from the analytical view-point, be any constant, real or complex. In particular, if ħ = i, the use of an algebra with the commutation relation leads to an elementary solution of the real equation of parabolic type

Proceedings of the Royal Society of Edinburgh Section A Mathematical and Physical SciencesJan 1, 19410 citations

Summary of IV

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Summary of IV

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