摘要:

The behavior of variational procedures for bound states is well understood, when using harmonic oscillator wave functions whose frequency ω is the only parameter. The same procedure, when applied to problems that have resonant states, shows a completely different behavior. By analyzing thes‐wave problem for a cavity potential of the formb′δ(r′−a), we show that, as a function of ω, it gives rise to plateaus that correspond to the real part of the resonant energies, assuming values ofb′ related to very narrow resonances compared with their separations. If the latter condition holds, the procedure seems generalizable to other types of potentials.

ISSN:0002-9505    

DOI:10.1119/1.18160

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

In a purely nonrelativistic formulation, a Hamiltonian is obtained for the description of states of a charged particle with spin, interacting with an external electromagnetic field. For the specific cases of spin‐1/2 and spin‐1, the simplest choices for the Hamiltonian functions lead to a value for the (lowest order) intrinsic magnetic moment equal to the Bohr magneton in both cases. This is the same as is obtained in treatments that start from a relativistic formulation, as in the Dirac theory. The nonrelativistic and relativistic formulations both employ the ‘‘minimal coupling principle,’’ but the resulting Hamiltonians with couplings are, for very general considerations, not completely determined. However, the corresponding ambiguity that occurs in the nonrelativistic theory is also present in the relativistic formulation. The simpler nonrelativistic theory is more transparent in exhibiting these features of the problem and dispels the notion that spin (and the associated magnetic moment) require relativistic formulations for a proper understanding.

ISSN:0002-9505    

DOI:10.1119/1.18161

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

We present a simple integrated circuit model of an excitable nerve axon based on a rotating switch. The heart of the circuit consists of two integrated circuits—a dual rotating switch and a quad comparator. Both the passive and active response of a segment of axon membrane are modeled. A single segment exhibits passive cable behavior up to a threshold voltage. Once threshold is reached, the segment ‘‘fires,’’ i.e., currents representative of sodium and potassium depolarizing and repolarizing currents flow sequentially. Furthermore, successive segments have been connected to model an extended section of excitable axon. A linear array of light emitting diodes (LEDs) connected to each segment allows the voltage on that segment to be visibly monitored. When mounted as a two‐dimensional LED array, this results in a ‘‘spatial oscilloscope’’ which shows the action potential propagating along the axon. The circuit could serve as a teaching tool for both the biophysics of nerve signal propagation and for electronics. It has the virtue of being relatively simple to understand as it is based on a rotating switch.

ISSN:0002-9505    

DOI:10.1119/1.18162

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

A model of a chiral isotropic medium (a gas of randomly oriented handed molecules) is presented, which allows exact calculation of the optical rotation.

ISSN:0002-9505    

DOI:10.1119/1.18266

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

The problem of prediction of the equilibrium state in an isolated composite system with an adiabatic internal wall is a delicate problem, whose solution is easily seen to be not entirely determined in the frame of elementary thermodynamics. We show how this indeterminacy can be removed by introducing a suitable kinetic model, in which the influence of the finite velocity of the wall on the change of momentum of the gas molecules impinging on it plays a relevant role. An interesting feature of the entropy behavior of the system is discussed.

ISSN:0002-9505    

DOI:10.1119/1.18163

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

We present an instructional undergraduate laboratory that introduces the student to an acousto‐optic modulator (AOM) in the context of an optical heterodyning experiment. A moving diffraction grating is used to illustrate the internal functioning of an acousto‐optic modulator and to make optical heterodyning experiments accessible to any undergraduate laboratory. The concepts and techniques presented can be used from the introductory through advanced level, in that, students gain direct laboratory experience with diffraction, the Doppler shift of light, construction of a Mach–Zehnder interferometer, optical path length measurements using a heterodyne technique, and sophisticated data analysis techniques.

ISSN:0002-9505    

DOI:10.1119/1.18164

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

Relativistic transformation equations for the 3‐vector force are derived from the Lorentz force law by using the well‐known transformation equations for electromagnetic fields and velocity. The derivation is a simple alternative to the conventional derivation based on relativistic expressions for energy and momentum.

ISSN:0002-9505    

DOI:10.1119/1.18165

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

We present the results of a simple experiment suitable for the undergraduate laboratory in which the onset of turbidity when an aniseed‐based liquor is diluted with water is observed. The optical transmission shows the behavior typical of the order parameter in a second‐order phase transition. The changes in the transmission are due to the precipitation of terpenes and the amount of precipitated terpenes also shows critical behavior of the formn=k′(c−cc)y, wherecis the fraction of water in the solution. The critical exponent is determined to bey=1.01±0.06.

ISSN:0002-9505    

DOI:10.1119/1.18166

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

An exact equation for the angular momentum states of the diatomic molecule is derived. The eigenstates of the idealized Hund’s cases (a) and (b) are then calculated from the exact result. Example calculations of the matrix elements of the rotational Hamiltonian in the Hund’s case (a) basis are given and Hönl–London factors for (a)↔(a) and (b)↔(b) transitions are calculated. All calculations are carried out within the fully standard theory of angular momentum. Previous discussions of diatomic angular momentum states have invariably employed special methods such as consistently applied anomalies, and it is not generally known that such methods are unnecessary.

ISSN:0002-9505    

DOI:10.1119/1.18167

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

A self‐contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of the method is derived and then a numerical algorithm is formulated. The algorithm is applied to determine the ground state of the harmonic oscillator, the Morse oscillator, the hydrogen atom, and the electronic ground state of the H+2ion and of the H2molecule. A computer program on which the sample calculations are based is available upon request.

ISSN:0002-9505    

DOI:10.1119/1.18168

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP