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Load:
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1. komponenta
| Lecture type | Total |
| Lectures |
30 |
| Seminar |
30 |
* Load is given in academic hour (1 academic hour = 45 minutes)
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Description:
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COURSE IMPLEMENTATION PROGRAM
1. A brief historical overview of the natural phenomena whose interpretations led to the establishment of i
development of quantum physics. Black body radiation, photoelectric effect, Planck hypothesis.
2. Heisenberg uncertainty relations. Operators and matrices. Hilbert space. Hermitic
operators. Schrödinger equation and boundary conditions on the wave function. Interpretation of the wave
functions. Infinitely deep potential pit.
3. Wave packet. Eigenvectors. The operator of evolution.
4. Quantum mechanical current and continuity equation. Scattering states and bound states in
one dimension. Potential step. Potential barrier. Conditions
continuity of the wave function. Coefficients of repulsion (reflection) and transmittance (transmission).
5. Bound states. Potential pit of final depth. Conditions for the existence of bound states. In short
about special functions. Airy functions. Particle in a homogeneous gravitational field.
6. Harmonic oscillator. Solving the Schrödinger equation. Algebraic mode of quantization
harmonic oscillator. Creation and undo operators. Particle number operator.
7. Angular momentum operator. Quantum mechanical rotator. Eigenvectors and eigenvalues
angular momentum operator.
8. Centrally symmetric potentials. Sphere functions. Radial Schrödinger equation.
9. Two-particle systems. Hydrogen atom and hydrogen-like atoms.
10. Stern-Gerlach experiment. Spin electron. Spin states and spin part of the wave function.
11. Addition of angular momentum and / or spins. Multielectronic systems and the Pauli principle.
Lithium atom.
12. Approximate methods in quantum mechanics. Perturbation account.
13. Calculation of variation.
14. Virial theorem. Hellmann-Feynman theorem. Molecules and Born-Oppenheimer
approximation.
15. Software packages for quantum chemical calculations.
DEVELOPING GENERAL AND SPECIAL COMPETENCES OF STUDENTS
General competencies: knowledge and recognition of phenomena and their mathematical description
Special competencies: application of quantum mechanics in technology.
STUDENTS 'TEACHING OBLIGATIONS AND THEIR PERFORMANCE
Students are required to attend lectures and seminars
CONDITIONS FOR OBTAINING A SIGNATURE
80% attendance at lectures and seminars
TEACHING METHODS
lectures (ex cathedra)
seminars (ex cathedra)
METHODS OF TESTING KNOWLEDGE AND TAKING EXAMS
Two optional written tests and homework. Students can choose the seminar topic themselves. Quality and skill of processing and presenting the seminar topic and the total number
points obtained at the colloquia define the final grade as follows:
0-39 insufficient
40-54 sufficient
55-69 good
70-84 very good
85-100 (or more) excellent
Students who earn 39, or less, points in colloquia, and who have not taken a seminar topic,
they must take a written and oral exam.
METHOD OF MONITORING THE QUALITY AND PERFORMANCE OF COURSES
Student survey
METHODOLOGICAL PREREQUISITES
None
COURSE LEARNING OUTCOMES
1. Determination of the Schrödinger equation for different systems, of one or more particles
2. Determining the mathematical space in which quantum mechanical problems are set and solved
3. Methods of solving the Schrödinger equation.
4. The meaning and significance of quantum numbers. Atomic and molecular orbitals.
LEARNING OUTCOMES AT PROGRAM LEVEL
1. Identify problems in which quantum effects cannot be ignored, as well as those in which
these effects can be ignored.
2. Distinguish classical quantities from corresponding quantum mechanical quantities, at the same time
retaining a physical dawn based on classical physics.
3. Recognition of the essential identity of the solution of the Schrödinger equation for one and the same
a particular problem, if the solutions differ only in the mathematical space in which it is
problem defined.
4. Application of exact and approximate quantum numbers to atomic and molecular systems.
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Learning outcomes:
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- Identify problems in which quantum effects cannot be ignored, as well as those in which these effects can be ignored.
- Distinguish classical quantities from corresponding quantum mechanical quantities, at the same time retaining a physical dawn based on classical physics.
- Recognition of the essential identity of the solution of the Schrödinger equation for one and the same a particular problem, if the solutions differ only in the mathematical space in which it is problem defined.
- Application of exact and approximate quantum numbers to atomic and molecular systems.
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Literature:
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Ira N. Levine, "Quantum Chemistry", 5th ed., Prentice-Hall, Inc. 2000.,
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V. Dananić, nastavni tekstovi na mrežnim stranicama FKIT-a,
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Fundamentals of Quantum Chemistry--Molecular Spectroscopy and Modern Electronic Structure Computations, Michael Mueller, Kluwer Academic Publishers, 2002.
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Pristupačnost
