BEHAVIOR OF SOUND WAVES IN SHEPHERD FLUTE ON THE BASIS OF QUANTUM THEORY OF INDIVIDUAL PHONONS

2010 ◽  
Vol 24 (17) ◽  
pp. 3439-3452
Author(s):  
SONJA KRSTIĆ ◽  
VJEKOSLAV SAJFERT ◽  
BRATISLAV TOŠIĆ
Keyword(s):  
Quantum Theory ◽  
Hyperbolic Equation ◽  
Plane Waves ◽  
Sound Waves ◽  
High Frequencies ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation ◽  
Theory And Experiment ◽  
Good Agreement

Using the linearized Hamiltonian of individual phonon, it was shown that Schrödinger's equation of individual phonon is by form identical with classical hyperbolic equation. It was also shown that damper in shepherd's flute is reflexive for high frequencies and transparent for low ones. This result was experimentally tested by authors and good agreement of theory and experiment was found. The propagation of sound in parallelopipedal and cylindrical shepherd's flute was investigated. It turned out that parallelopipedal sound propagates in z-direction, only, while in cylindrical one besides plane waves in z-direction the damped waves in x, y plane appear.

Sound Propagation in Dilute Polyatomic Gases

1972 ◽  
Vol 27 (4) ◽  
pp. 583-592
Author(s):  
H. Moraal ◽  
F. Mccourt
Keyword(s):  
Pressure Range ◽  
Sound Propagation ◽  
Plane Waves ◽  
Point Of View ◽  
Perturbation Function ◽  
Sound Waves ◽  
Polyatomic Gas ◽  
Measured Pressure ◽  
Theory And Experiment ◽  
Good Agreement

Abstract Sound propagation in dilute pure gases, both monatomic and polyatomic, has been considered from the point of view of the Waldmann-Snider equation. It is shown that the commonly employed assumption that sound propagation in gases is equivalent to the propagation of plane waves is valid only in the region where collisions restore equilibrium faster than it is perturbed by the sound waves. A systematic truncation procedure for an expansion of the perturbation function in irreducible Cartesian tensors is introduced and then illustrated in solutions for three specific kinds of molecules, helium, nitrogen and rough spheres. The agreement between theory and experiment is rather good for sound absorption in the region where the ratio of the collision and sound frequencies is greater than 1.5. The agreement in the case of dispersion is good over the whole measured pressure range. One useful result obtained is to show the polyatomic gas calculations in second approximation have as good agreement with experiment as the calculations for noble gases in third approximation. This can be related to the possession by the polyatomic gas of a bulk viscosity which dominates in sound propagation.

scholarly journals Bound State of Heavy Quarks Using a General Polynomial Potential

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Hesham Mansour ◽  
Ahmed Gamal
Keyword(s):  
Bound States ◽  
Bound State ◽  
Heavy Quarks ◽  
Polynomial Potential ◽  
Schrödinger’S Equation ◽  
General Polynomial ◽  
L Value ◽  
Schrödinger's Equation ◽  
Better Than ◽  
Good Agreement

In the present work, the mass spectra of the bound states of heavy quarks cc-,bb-, and Bc meson are studied within the framework of the nonrelativistic Schrödinger’s equation. First, we solve Schrödinger’s equation with a general polynomial potential by Nikiforov-Uvarov (NU) method. The energy eigenvalues for any L- value is presented for a special case of the potential. The results obtained are in good agreement with the experimental data and are better than previous theoretical studies.

A Theory of Hartree's Atomic Fields

1928 ◽  
Vol 24 (2) ◽  
pp. 328-342 ◽  
Author(s):  
J. A. Gaunt
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
Potential Energy ◽  
Unit Volume ◽  
Wave Functions ◽  
The Other ◽  
Schrödinger’S Equation ◽  
Energy Parameters ◽  
Old Quantum Theory ◽  
Schrödinger's Equation

In a recent communication to this Society Dr Hartree has put forward a method for calculating the field of anatom containing many electrons. Each orbit—to borrow a metaphor from the old quantum theory—is related to a wave-function Ψ which obeys Schrödinger's equation. The potential energy used in this equation is due partly to the field of the nucleus, and partly to the fields of the electrons in the other orbits. The latter are calculated upon Schrödinger's interpretation of the wave-function, that |Ψ|2 is the density of charge, measured in electronic charges per unit volume. It is not the purpose of this paper to discuss the practical methods of obtaining wave-functions which reproduce the fields from which they are derived; but to relate these wave-functions and their energy parameters to those of the accepted theory.

scholarly journals Reducing a Class of Two-Dimensional Integrals to One-Dimension with an Application to Gaussian Transforms

Atoms ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 53
Author(s):  
Jack C. Straton
Keyword(s):  
Quantum Theory ◽  
Arbitrary Function ◽  
Plane Waves ◽  
Wave Functions ◽  
One Dimension ◽  
Two Dimensional ◽  
Transition Amplitudes ◽  
Multidimensional Integrals ◽  
Coulomb Potentials

Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers multiplied by an arbitrary function of xy/(x+y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, and Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.

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