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Lecture

Quantum Mechanics: Energy Levels

In course

BIO-443: Fundamentals of biophotonics

This module serves as an introduction to the area of biophotonics. The approach is multidisciplinary .The course is mainly knowledge-based but students will benefit from the skills learned by carrying out problem solving and by completing the assignment. ...

Description

This lecture covers the behavior of particles subject to potential energy, as described by the Schrodinger equation. It delves into the energy levels of hydrogen-like atoms, the Schrodinger equation in spherical coordinates, and the solution of the radial equation for hydrogen atoms. The lecture also explores quantum numbers, molecular bonding, and spectra, including vibrational and rotational states. The discussion extends to the formation of molecules, ionic and covalent bonds, hydrogen bonds, and metallic bonds. Additionally, it touches on the stability of closed electronic shells, the concept of probability distribution functions, and the study of vibrations and rotations in atoms and molecules.

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Instructor

Aleksandra Radenovic

From April 2021 Full Professor 2015 -2021 Associate Professor2008-2015 Tenure-Track Assistant Professor2004-2007 Postdoc at the University of California, Berkeley in the group of Prof.Liphardt2003 PhD student of Prof. Dietler in Laboratory of Physics of Living Matter, University of Lausanne 1999 Diploma thesis on the subject of the Raman spectroscopy of beta carotene1994-1999 Physics department at the University of Zagreb1994 baccalaureate, Classical gymnasium

Official source

Ontological neighbourhood

Physics

Atomic physics: Topics in atomic physics

Related concepts (32)

Hydrogen atom

A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the baryonic mass of the universe. In everyday life on Earth, isolated hydrogen atoms (called "atomic hydrogen") are extremely rare. Instead, a hydrogen atom tends to combine with other atoms in compounds, or with another hydrogen atom to form ordinary (diatomic) hydrogen gas, H2.

Chemical bond

A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules, crystals, and other structures. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of electrons as in covalent bonds. The strength of chemical bonds varies considerably; there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force, and hydrogen bonding.

Energy level

A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules.

Molecular vibration

A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 1013 Hz to approximately 1014 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm−1 and wavelengths of approximately 30 to 3 μm. For a diatomic molecule A−B, the vibrational frequency in s−1 is given by , where k is the force constant in dyne/cm or erg/cm2 and μ is the reduced mass given by .

Hydrogen bond

In chemistry, a hydrogen bond (or H-bond) is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing a lone pair of electrons—the hydrogen bond acceptor (Ac). Such an interacting system is generally denoted , where the solid line denotes a polar covalent bond, and the dotted or dashed line indicates the hydrogen bond.

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Untitled

Molecular Polarity and Valence Bond Theory