**CHM 642: Principles of Quantum Chemistry**** ****(4)**

**Prerequisites: **MTH 101, PHY 101, CHM 101, MTH 102, PHY 102, MTH 201, PHY 201 or their equivalent** Not allowed for Physics majors**

*Review of basic concepts of quantum theory: *wave-particle duality and de Broglie wavelengths, uncertainty principle, superposition and state of a quantum system.

*Mathematical background:* Operators in quantum mechanics and their properties, eigenvalues and eigenfunctions, commutation relations, unitary transformations and change of basis. Matrix representation of operators.

*Postulates of quantum mechanics***:** States and wavefunctions, observables and the measurement hypothesis, Born interpretation of wavefunction, time evolution of states and the Schrodinger equation, stationary states, compatible observables and the generalized uncertainty principle.

*One-dimensional problems***:** Particle in a well and transmission through a barrier. Probability currents and the equation of continuity. Two and three-dimensional potential wells and degeneracy. Applications to conjugated molecules and other one-dimensional systems. Linear harmonic oscillator – ladder operator method, parity of harmonic oscillator eigenfunctions. Rigid rotor problem, angular momentum, angular momentum eigenvalues and eigenfunctions.

*The hydrogen atom:* Atomic orbitals – radial and angular wavefunctions and distributions, electron-spin and spin operators. Virial theorem and application to hydrogen atom and other problems. Hydrogen-like atoms.

*Atoms in external fields:* Zeeman and Stark effect.

*Approximation methods:* Time-independent perturbation theory – Anharmonic oscillator, He atom, H^{2+} molecular ion. Variational theorem - He atom, H^{2+} molecule and the LCAO approach.

*Suggested Books*:

- Levine, I.,
*Quantum Chemistry*, Ed. 6th, Pearson Press,**2009**. - McQuarrie, D. A.,
*Quantum Chemistry*, Ed. 2nd*,*University Science Books,**2008**. - Zettili, N.,
*Quantum*Mechanics, Ed. 2nd, John Wiley,**2009**. - Atkins, P. W., Friedman, R. S.,
*Molecular Quantum Mechanics*, Oxford University Press,**2008**.

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