Fringes decorating anticaustics in ergodic wavefunctions

1989 ◽  
Vol 424 (1867) ◽  
pp. 279-288 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Energy Range ◽  
Probability Density ◽  
Integrable Systems ◽  
Chaotic Systems ◽  
Planck’S Constant ◽  
Diffraction Patterns ◽  
Definition Of ◽  
Planck's Constant

The probability density Π is calculated for quantum eigenstates near spatial boundaries of classically chaotic regions. By contrast with integrable systems, for which the classical Π diverges on classical boundaries, which are caustics, in chaotic systems the classical Π does not diverge but vanishes abruptly in a way that depends on the number of freedoms N ; the boundaries are anticaustics. Quantum mechanics softens anticaustics, to give Π in terms of a set of canonical diffraction patterns, one for each N ; these are studied in detail. The appropriate definition of Π involves averaging over eigenstates in an energy range larger than O ( h ) but smaller than O ( h ⅔ ) (where h is Planck’s constant), that is over a range of ∆ N states near the N th, where N 1-1 / N ≪ ∆ N ≪ N 1-⅔ N .

Mass gap problem and Planck constant

2021 ◽  
Vol 34 (3) ◽  
pp. 385-388
Author(s):  
Amrit S. Šorli ◽  
Štefan Čelan
Keyword(s):  
Quantum Mechanics ◽  
Einstein Relation ◽  
Planck Constant ◽  
Planck’S Constant ◽  
Mass Gap ◽  
Planck's Constant

The mass gap problem is about defining the constant that defines the minimal excitation of the vacuum. Planck’s constant is defining the minimal possible excitation of the vacuum from the point of quantum mechanics. The mass gap problem can be solved in quantum mechanics by the formulation of the photon’s mass according to the Planck‐Einstein relation.

Heisenberg, Bohr, Robertson, and the Uncertainty Principle

2020 ◽  
pp. 133-156
Author(s):  
Jim Baggott
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Laboratory Experiments ◽  
Space Time ◽  
Spectral Lines ◽  
Planck’S Constant ◽  
Classical Space ◽  
Planck's Constant

From the outset, Heisenberg had resolved to eliminate classical space-time pictures involving particles and waves from the quantum mechanics of the atom. He had wanted to focus instead on the properties actually observed and recorded in laboratory experiments, such as the positions and intensities of spectral lines. Alone in Copenhagen in February 1927, he now pondered on the significance and meaning of such experimental observables. Feeling the need to introduce at least some form of ‘visualizability’, he asked himself some fundamental questions, such as: What do we actually mean when we talk about the position of an electron? He went on to discover the uncertainty principle: the product of the ‘uncertainties’ in certain pairs of variables—called complementary variables—such as position and momentum cannot be smaller than Planck’s constant h (now h / 4π‎).

New test of quantum mechanics: Is Planck’s constant unique?

1991 ◽  
Vol 66 (3) ◽  
pp. 256-259 ◽  
Author(s):  
Ephraim Fischbach ◽  
Geoffrey L. Greene ◽  
Richard J. Hughes
Keyword(s):  
Quantum Mechanics ◽  
Planck’S Constant ◽  
Planck's Constant

scholarly journals AN ENTROPIC PICTURE OF EMERGENT QUANTUM MECHANICS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250048 ◽  
Author(s):  
D. ACOSTA ◽  
P. FERNÁNDEZ DE CÓRDOBA ◽  
J. M. ISIDRO ◽  
J. L. G. SANTANDER
Keyword(s):  
Quantum Mechanics ◽  
Quantum Mechanical ◽  
Entropy Flow ◽  
Planck’S Constant ◽  
Formal Derivation ◽  
Usual Quantum ◽  
Holographic Screen ◽  
Holographic Screens ◽  
Planck's Constant ◽  
Emergent Quantum Mechanics

Quantum mechanics emerges à la Verlinde from a foliation of ℝ3 by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantized in units of Boltzmann's constant kB. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on ℝ3. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant ℏ from Boltzmann's constant kB.

scholarly journals Quantity in Quantum Mechanics and the Quantity of Quantum Information

2021 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Density Distribution ◽  
Probability Density ◽  
Hermitian Operator ◽  
Space Time ◽  
Complex Hilbert Space ◽  
Probability Density Distribution ◽  
Classical Quantum ◽  
Definition Of

The paper interprets the concept “operator in the separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined in the “classical” quantum mechanics) by that of “quantum information”. As far as wave function is the characteristic function of the probability (density) distribution for all possible values of a certain quantity to be measured, the definition of quantity in quantum mechanics means any unitary change of the probability (density) distribution. It can be represented as a particular case of “unitary” qubits. The converse interpretation of any qubits as referring to a certain physical quantity implies its generalization to non-Hermitian operators, thus neither unitary, nor conserving energy. Their physical sense, speaking loosely, consists in exchanging temporal moments therefore being implemented out of the space-time “screen”. “Dark matter” and “dark energy” can be explained by the same generalization of “quantity” to non-Hermitian operators only secondarily projected on the pseudo-Riemannian space-time “screen” of general relativity according to Einstein's “Mach’s principle” and his field equation.

Black-Body Radiation

2019 ◽  
pp. 322-330
Author(s):  
Robert H. Swendsen
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum ◽  
Electromagnetic Radiation ◽  
Black Body ◽  
Black Body Radiation ◽  
Perfect Absorber ◽  
Max Planck ◽  
Planck’S Constant ◽  
Light Waves ◽  
Planck's Constant

A black body is a perfect absorber of electromagnetic radiation. The energy spectrum was correctly calculated by Max Planck under the assumption that the energy of light waves only came in discrete multiples of a constant (called Planck’s constant) times the frequency. This was perhaps the first achievement of quantum mechanics. The derivation is presented here. The purpose of the current chapter is to calculate the spectrum of radiation emanating from a black body. The calculation was originally carried out by Max Planck in 1900 and published the following year. This was before quantum mechanics had been invented, or perhaps it could be regarded the first step in its invention.

scholarly journals The Geometric Algebra Lift of Qubits and Beyond

2022 ◽  
Author(s):  
Alexander Soiguine
Keyword(s):  
Quantum Mechanics ◽  
Geometric Algebra ◽  
Wave Diffraction ◽  
Three Dimensions ◽  
Quantum Mechanical ◽  
Complex Numbers ◽  
Interpretation Of Quantum Mechanics ◽  
Diffraction Patterns ◽  
Definition Of

The Geometric Algebra formalism opens the door to developing a theory upgrading conventional quantum mechanics. Generalizations, stemming from implementation of complex numbers as geometrically feasible objects in three dimensions; unambiguous definition of states, observables, measurements bring into reality clear explanations of conventional weird quantum mechanical features, particularly the results of double split experiments where particles create diffraction patterns inherent to wave diffraction. This weirdness of the double split experiment is milestone of all further difficulties in interpretation of quantum mechanics.

Dualism QM and GR

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Noncommutative Geometry ◽  
Quantum Tunneling ◽  
Closed Surface ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Surface Integral ◽  
Definition Of

Quantum tunneling of noncommutative geometry gives the definition of time in the form of holography, that is, in the form of a closed surface integral. Ultimately, the holography of time shows the dualism between quantum mechanics and the general theory of relativity.

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