Course title
量子力学Ⅱ   [Quantum Mechanics Ⅱ]
Course category	technology speciality courses,ets.	Requirement		Credit	2
Department		Year	3～4	Semester	Fall
Course type	Fall	Course code	023613
Instructor(s)
鵜飼 正敏   [UKAI Masatoshi]
Facility affiliation	Faculty of Engineering	Office		Email address

Course description

Based on the mathematical basis completed in the course "Quantum Mechanics I", the quantum-mechanical description of one electron in central field, i.e., the theory of hydrogenic atoms is given as a typical example of the 3 dimensional quantum systems.

Expected Learning

1) To become able to build a Schrodinger equations for a particle in the the 3 dimensional space. 2) To become able to separate multi-variables differential equation into a set of one dimensional equations. 3) To become able to derive the spherical harmonics and to identify them as the wave funtions corresponding to angular momenta. 4) To become able to derive the radial wave functions for electrons in the central coulomic field corresponding to the eigen values of total mechanical energies.

Course schedule

(1) Basic concept on the Schrodinger equation; revision of one dimensional equations and its expansion into the 3 dimensional cases. (2) Hamiltonian of two particle in laboratory frame and the separation of its Schrodinger equation into the equations for center-of-mass motion and relative motion. (3) The Schrodinger equation for particle in the central field. 　　(3-1) The concept of the central field and angular momenta. 　　(3-2) Separation of variables. (4) The way to derive the spherical harmonics. 　　(4-1) The Legendre differential equation and its solution. 　　(4-2) The associated Legendre differential equation and its solution. 　　(4-3) Examples of the sperical harmonics and their properties. 　　(4-4) Angular momenta and rotational operations. 　　(4-5) Properties of angular momentum operators. (5) The way to derive the radial wave functions. 　　(5-1) Effective potentials. 　　(5-2) Asymptotic behavior of radial functions in effective potentials. 　　(5-3) Derivation of the associated Laguerre differential equation and its eigen value. 　　(5-4) The solutions of the Laguerre differential equation. 　　(5-5) The solutions of the associated Laguerre differential equation. 　　(5-6) Comparison of the solutions with the Bohr model.

Prerequisites

Although it is not necessary to complete the credits of the courses "Introduction to Quantum Mechanics" and "Quantum Mechanics I", the idea and method given in those courses are used as common. So it is necessary to understand the contents of the courses "Introduction to Quantum Mechanics" and "Quantum Mechanics I".

Required Text(s) and Materials

Not specified. Every typical textbook of quantum mechanics describes the theory for hydorgenic atoms.

References

Theoretical bases are mainly taken from B.H.Bransden&J.Joachain, "Physics of Atoms and Molecules, 2nd Ed." (2009,Prentice Hall) and W. Greiner, "Quantum Mechnics, An Introduction, 4th Ed." (2001,Springer). However, detailed derivations are taken elsewhere.

Assessment/Grading

Evaluated by homeworks and a semester examination.

Message from instructor(s)

Quantum mechanics is one of the methods to solve physical phenomena into elementary problems. It looks complicated at a first glance. However, if you confirm the each steps of derivation, you will be surprised that the theory is constructed with plain methmatical methods, so that it is highly understandable. We remark that the way of quantum-mechanical understanding on the natural phenomena will be your most important capability for a physical engineer.

Course keywords

3 dimensional systems, central field, hydrogenic atoms, spherical harmonics, angular momenta, and associated Laguerre polynomials.

Office hours

Welcome at any time, but make an appointment beforehand by email.

Remarks 1

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Lecture Language

Japanese

Language Subject

Last update

3/20/2018 1:29:17 PM