| Course title | |||||
| 量子力学Ⅱ [Quantum Mechanics Ⅱ] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 2 | |
| Department | Year | 3～4 | Semester | 3rd | |
| Course type | 3rd | Course code | 023613 | ||
| Instructor(s) | |||||
| 鵜飼 正敏 [UKAI Masatoshi] | |||||
| Facility affiliation | Faculty of Engineering | Office | Email address | ||
| Course description |
| Among the theoretical foundations for studying the Applied Physics, Quantum Mechanics is the theory of understanding microscopic phenomena from the viewpoints of the particle/wave duality, the uncertainty principle, and so on. 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. See the Curriculum maps. |
| Course schedule |
|
Expansion of the idea of mechanical system into the three dimension. (1st class) Basic concept on the Schroedinger equation; revision of one dimensional equations and its expansion into the 3 dimensional cases. (2nd class) 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. (3rd class) The Schrodinger equation for particle in the central field. (a) The concept of the central field and angular momenta. (b) Separation of variables. The way to derive the spherical harmonics. (4th class) Separation of angular variables and derivation of the Legendre differential equation. (5th class) The solutions of the Legendre differential equation and the associated Legendre differential equation. (6th class) Examples of the sperical harmonics and their properties. (7th class) Angular momenta and rotational operations. (8th class) Relations of the rotational operations with the angular momentum operators (9th class) Properties of angular momentum operators. The way to derive the radial wave functions. (10th class) Effective potentials in the coulombic field and the aymptotic behaviors of radial wave functions in those potentials. (11th class) Derivation of the associated Laguerre differential equation and its eigen values. (12th class) The solutions of the Laguerre differential equation. (13th class) The solutions of the associated Laguerre differential equation. (14the class) Comparison of the radial distribution functions with the Bohr model. (15th class) The properties of the hydrogenic wave function. Conclusions. |
| 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". Students are expected to have the standard amount of time to prepare for and review the lecture as specified by the University. |
| 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 (1) homeworks and (2) a semester examination. The weight of evaluation between (1) to (2) is approximately 1 to 3. |
| 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. Office: Bld. No.4, rm.510. Email: ukai3 |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/18/2019 2:59:06 PM |