Quantum Mechanics: Schrödinger Equation

This lecture covers the Schrödinger Equation, which describes the total energy of quantum systems in terms of kinetic and potential energy operators. It explains the time-dependent and time-independent Schrödinger equations, approximations to solve them, quantum numbers, exclusion principle, atomic orbitals, and molecular orbital theory. The lecture also discusses valence electrons, VSEPR model, valence bond theory, hybridization, formation of carbon-carbon bonds, molecular orbital energy diagrams, and the complementarity of Valence Bond and Molecular Orbital theories.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related lectures (58)

Related concepts (35)

MSE-486: Organic electronic materials

This course will introduce students to the field of organic electronic materials. The goal of this course is to discuss the origin of electronic properties in organic materials, charge transport mecha

Molecular orbital

In chemistry, a molecular orbital (ɒrbədl) is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms atomic orbital and molecular orbital were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions. At an elementary level, they are used to describe the region of space in which a function has a significant amplitude.

Quantum number

In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be known with precision at the same time as the system's energy—and their corresponding eigenspaces. Together, a specification of all of the quantum numbers of a quantum system fully characterize a basis state of the system, and can in principle be measured together.

Principal quantum number

In quantum mechanics, the principal quantum number (symbolized n) is one of four quantum numbers assigned to each electron in an atom to describe that electron's state. Its values are natural numbers (from 1) making it a discrete variable. Apart from the principal quantum number, the other quantum numbers for bound electrons are the azimuthal quantum number l, the magnetic quantum number ml, and the spin quantum number s. As n increases, the electron is also at a higher energy and is, therefore, less tightly bound to the nucleus.

Antibonding molecular orbital

In theoretical chemistry, an antibonding orbital is a type of molecular orbital that weakens the chemical bond between two atoms and helps to raise the energy of the molecule relative to the separated atoms. Such an orbital has one or more nodes in the bonding region between the nuclei. The density of the electrons in the orbital is concentrated outside the bonding region and acts to pull one nucleus away from the other and tends to cause mutual repulsion between the two atoms.

Molecular orbital theory

In chemistry, molecular orbital theory (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century. In molecular orbital theory, electrons in a molecule are not assigned to individual chemical bonds between atoms, but are treated as moving under the influence of the atomic nuclei in the whole molecule. Quantum mechanics describes the spatial and energetic properties of electrons as molecular orbitals that surround two or more atoms in a molecule and contain valence electrons between atoms.

Molecular Orbitals: Bonding and Hybridization MSE-486: Organic electronic materials

Explores the transition from atomic to molecular orbitals, covering quantum systems, approximations, valence electrons, and covalent bonds.

Crystal Field Theory: Spectrochemical Series CH-222: Coordination chemistry

Explores the Spectrochemical Series for metals and ligands, Crystal Field Splitting, Jahn-Teller distortion, and bonding interactions in coordination compounds.

Atomic Structure: Quantum Mechanics CH-160(en): Advanced general chemistry (english)

Covers atomic theory, Schrödinger equation, quantum numbers, electron configurations, and periodic properties of elements.

Quantum Mechanical Model: Wavefunction MSE-431: Physical chemistry of polymeric materials

Explores the Quantum Mechanical Model, including wave-particle duality, the uncertainty principle, and electron orbitals.

Ligand Field Theory: Crystal Field Splitting CH-222: Coordination chemistry

Delves into ligand field theory, crystal field splitting, and molecular orbitals in transition metal complexes.