摘要:

A numerical method for the solution of one‐dimensional Schrödinger‐like equations with arbitrary numerical or analytical potentials is presented. The method takes advantage of matrix algebra for both obtaining several eigenvalues and eigenvectors at the same time and saving computer time. On the other hand, the method illustrates the close relationship between differential and algebraic eigenvalue problems, as well as the mathematical origin of quantization. Several examples are worked out in the text and the procedure for applying a user friendly routine to other problems is given.

ISSN:0002-9505    

DOI:10.1119/1.18242

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

We argue that introducing the reciprocal lattice as the Fourier transform of the Bravais lattice provides not only a concise definition for the reciprocal lattice, but also makes it a concept easy to grasp. To illustrate the power of the concept we derive the reciprocal lattices of the bcc and fcc structures directly from their conventional unit cells, rather than from the primitive unit cells.

ISSN:0002-9505    

DOI:10.1119/1.18243

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

We describe an undergraduate laboratory experiment developed for sophomore modern physics students, using the x‐ray analysis feature of a scanning electron microscope. The experiment described is a fundamental physics measurement performed with a state‐of‐the‐art apparatus not usually used in pedagogical physics experiments. The characteristic x‐ray spectrum of elements shows a simple progression that can be quantitatively explained by the conceptually important Bohr–Rutherford shell model of atomic structure. Students measure theKα andKβ x‐ray spectra from metals in the range of 12≤Z≤41. The measurements allow the verification of Moseley’s law scaling of x‐ray energies with atomic number and a quantitative measure of the data’s fit to the shell model.

ISSN:0002-9505    

DOI:10.1119/1.18244

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

摘要:

The motion of the elastic pendulum is ruled by coupling between the pendulum mode and the harmonic oscillator mode. The bob of the pendulum executes trajectories in a domain of the vertical plane, the shape and size of which are set by the initial conditions and the total energy of the pendulum. The limits of this libration, in exact resonance, are studied using parabolic coordinates. Other Hamiltonians, with similar interaction terms, exhibit similar libration limits.

ISSN:0002-9505    

DOI:10.1119/1.18245

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.18246

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.18425

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.18426

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP

ISSN:0002-9505    

DOI:10.1119/1.18427

出版商:American Association of Physics Teachers    

年代:1996

数据来源: AIP