摘要:

Given a gas ofN0hard‐sphere molecules in a vessel of volumeV0, one shows in a simple way that the probabilityWN0(N,V,V0) thatNmolecules are located in a subvolumeVofV0is given by the hypergeometric distribution. One shows that this distribution can be written as the product of the binomial distribution, which characterizes the ideal gas, and a factor which takes into account the size of the molecules. In the limit of low densities, one checks in two cases of practical interest that the derived distribution presents slight deviations from the corresponding ideal behavior.

ISSN:0002-9505    

DOI:10.1119/1.15234

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

In two dimensions the minimum energy configuration of a finite set of equal point charges confined to a circle does not necessarily have all the charges on the circumference. In three dimensions, however, we show that the minimum energy configuration of a similar set of charges confined by a surface has all of the charges located on the surface. The pseudo‐two‐dimensional analog of the three‐dimensional case, provided by an array of parallel line charges confined to a cylinder, is also investigated.

ISSN:0002-9505    

DOI:10.1119/1.15235

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

Instead of regarding the classical limit as the limit ℏ→0, an alternative view based on the physical interpretation of the elements of the density matrix is proposed. The derivation of the classical limit of quantum mechanics is carried out in two stages. First, the statistical classical limit is derived, and then, with an appropriate initial condition, the deterministic classical limit is obtained. The derivation hinges on the use of the Feynman path‐integral formulation of quantum mechanics in terms of the density matrix. It is shown that deterministic (Hamilton’s or Newton’s) classical mehanics is not the classical limit of Schrödinger’s wave mechanics. The classical limit of Schrödinger’s wave mechanics is only statistical and corresponds to the classical Liouville equation. In order to obtain the deterministic classical limit, it is necessary to start out initially with a quantum mechanical mixture.

ISSN:0002-9505    

DOI:10.1119/1.15236

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.15237

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.15238

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.15239

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

A modified WKB approximation is used to calculate the eigenvalues for the transverse modes of a nonuniform strength. (AIP)

ISSN:0002-9505    

DOI:10.1119/1.15240

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.15322

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

摘要:

The dispersion relation between angular frequency and wave number is derived for both deep and shallow water waves. (AIP)

ISSN:0002-9505    

DOI:10.1119/1.15241

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.15242

出版商:American Association of Physics Teachers    

年代:1987

数据来源: AIP