scholarly journals Elementary Theory of Quantum-Mechanical Collective Motion of Particles, II

1955 ◽  
Vol 13 (5) ◽  
pp. 482-496 ◽  
Author(s):  
Sin-itiro Tomonaga
Keyword(s):  
Collective Motion ◽  
Elementary Theory ◽  
Quantum Mechanical

scholarly journals An elementary theory of electronic semi-conductors, and some of their possible properties

1933 ◽  
Vol 140 (842) ◽  
pp. 505-522 ◽  
Keyword(s):  
Electric Power ◽  
Hall Coefficient ◽  
Elementary Theory ◽  
Formal Theory ◽  
Quantum Mechanical ◽  
Electronic Conduction ◽  
Thermo Electric ◽  
Conduction Electrons ◽  
Proposed Model ◽  
Independent Families

The formal theory of electronic semi-conductors was started by A. H. Wilson. It has recently been carried further by Bronstein, and has, of course, been applied (for example to the theory of rectifying contacts) and discussed in a number of other places. There is, however, I think, still room for a more general but quite elementary discussion of a number of possible models, all of which represent possible varieties of semi-conductors; it is to be understood throughout that only electronic conduction is in question. Granted certain general quantum mechanical theorems, the elementary theory can be made both simple and exact. After presenting such a version of the theory here, it is my purpose to show how the proposed model semi-conductors can account for the positive or negative or zero Hall coefficients which are observed, and also for the large positive or negative thermoelectric power of a semi-conductor-metal thermocouple and for the sign relationships of the two effects. The possibility of the explanation of an abnormal sign for the Hall coefficient is, of course, no new thing; it was first contemplated in the work of Peierls on metals and at his suggestion taken over (but not elaborated) by Bronstein ( loc. cit .) for semi-conductors. But a satisfactory (even elementary) theory requires us to consider the conduction in a solid as a mixed phenomenon due to two almost independent families of electrons. This has not been undertaken by Bronstein or by Peierls and such a theory is given here. It may prove of importance in further study of semi-conductors, beyond the phenomena on which attention is concentrated here. The scope of this paper then is as follows. We give an elementary theory of the effective number of “conduction” electrons in model semi-conductors of various types. We take account both of the few ordinary electrons in otherwise empty levels, and of the few holes or vacancies in otherwise completely full electron levels which function as positive electrons. We work out for semi conductors, conducting partly by electrons and partly by holes, the isothermal Hall coefficient and the thermo-electric power of the thermocouple formed by the semi-conductor and an ideal metal. We thus show in detail how abnormal signs of the Hall effect and the thermo-electric power can be fitted into the theory.

Collective motion in quantum mechanics

1957 ◽  
Vol 239 (1218) ◽  
pp. 399-412 ◽  
Keyword(s):  
Collective Motion ◽  
Electron Gas ◽  
Quantum Mechanical ◽  
Particle Model ◽  
Coupling Theory ◽  
Rotating System ◽  
Plasma Oscillations ◽  
Nucleon Recoil ◽  
The Moment ◽  
General Method

A general method of discussing quantum-mechanical problems involving collective motion is proposed, in which the emphasis is placed on consideration of sets of states rather than single states, and in which the additional collective co-ordinates are not redundant but used to describe the sets. The method is applied to a number of relatively simple examples: plasma oscillations of an electron gas; some problems of nuclear structure including the α-particle model and the collective model; and to two problems in meson field theory, concerning nucleon isobars in strong-coupling theory and concerning nucleon recoil. One of the main aims is to determine as well as possible the parameters of the collective motion; in particular, a formula is given for the moment of inertia of a rotating system.

Zur rotatorischen Bewegung eines Systems von n Massenpunkten. I

1968 ◽  
Vol 23 (10) ◽  
pp. 1419-1430
Author(s):  
H. Ruder ◽  
H. Volz
Keyword(s):  
Collective Motion ◽  
Frame Of Reference ◽  
Quantum Mechanical ◽  
Moments Of Inertia ◽  
Quantum Mechanical Treatment ◽  
Special Cases ◽  
System Of Particles ◽  
Coupling Terms ◽  
Rotational Motions ◽  
Limiting Case

The concept of rotational motion of a system of particles is strongly related to the existence of a frame of reference connected with the system in such a way that the coupling terms between the internal and the rotational motions vanish.This frame of reference, if existent, has to be uniquely defined independent of the type of motion by the configuration of the system only.It is shown that only in very special cases such a frame can be found. The existence of such a frame, however, is not sufficient for the appearance of a rotational structure in the energy spectrum of the system in quantum mechanical treatment. The importance of eliminating the coupling terms for the transition from the system of point masses to the limiting case of the rigid body is discussed. It is shown that in the case of exact decoupling the effective moments of inertia appearing in the Hamiltonian of the collective motion necessarily agree with the normal definition. It therefore seems inconsistent to neglect coupling terms and to take non-normal moments of inertia from the collective part alone.

Local interaction rules and collective motion in black neon tetra (Hyphessobrycon herbertaxelrodi) and zebrafish (Danio rerio).

2019 ◽  
Vol 133 (2) ◽  
pp. 143-155 ◽  
Author(s):  
Vicenç Quera ◽  
Elisabet Gimeno ◽  
Francesc S. Beltran ◽  
Ruth Dolado
Keyword(s):  
Danio Rerio ◽  
Collective Motion ◽  
Local Interaction

RELAXATION AND COLLECTIVE MOTION IN SUPERCONDUCTORS. A TWO-FLUID DESCRIPTION

1978 ◽  
Vol 39 (C6) ◽  
pp. C6-488-C6-489 ◽  
Author(s):  
C. J. Pethick ◽  
H. Smith
Keyword(s):  
Collective Motion ◽  
Two Fluid
Sign in / Sign up

Export Citation Format

Share Document