Quantum Mechanics and the Schrodinger Equation

Flashcards generated from lecture notes on the Schrodinger equation, particle in a box, harmonic oscillator, and application to hydrogen atoms and molecules.

Schrodinger Equation

An equation used to define the energy of a system using a wave function, containing all the information about that system.

Hamiltonian Operator

An operator that acts on a wave function to alter it, containing all the information that can be applied to the wave function to get the result (energy operating on the wave function).

Splitting the Hamiltonian

Dividing the Hamiltonian into kinetic and potential energy terms, applying classical concepts to quantum mechanics.

Heisenberg's Uncertainty Principle

We cannot know both position and momentum at the same time, but we can apply a wave function to understand how momentum is changing as the wave function moves.

Particle in a Box

A conceptual and mathematical way of showing how the Schrodinger equation works, involving a particle trapped in a confined area.

Harmonic Oscillator

A model showing how energy is quantized, applying to diatomic molecules and atoms in molecules with restoring force.

Boundary Conditions

At the edges of the box, the wave function equals zero, leading to the understanding of how wavelengths change as energy increases.

Permitted Wavelengths

The permitted wavelengths for a particle in a box, defined by the equation lambda = 2L/n.

Permitted Energies

The energy of a wave function within a particle in a box, defined by the equation E = n^2h^2 / 8mL^2.

Quantum Dots

Semiconducting nanoparticles that behave like particles in a box due to their small size, allowing for tuning of absorption properties.

Conjugated Molecules

Molecules with delocalized electrons across the molecule, creating a 'box' the length of the chain, allowing for calculation of energy levels

Potential Energy (Harmonic Oscillator)

The potential energy term in the harmonic oscillator, defined as potential energy equals 1/2 kx^2.

Zero Point Energy

The non-zero energy that a quantum system always has, even at absolute zero.

Hydrogen Atom

Simplified system with one proton and one electron, to which the Schrodinger equation is applied to calculate its properties.

Born-Oppenheimer Approximation

Approximation stating that the mass of the proton is so big that we can ignore the kinetic energy, focusing on the kinetic energy of the electron.

Applying Schrodinger Equation to Molecules

Considering the interactions between each electron and the nuclei, including attraction and repulsion forces.

Fixed Nuclei

Nuclei are frozen in space, simplifying the interactions considered in molecular calculations.

Quantization of Energy

Energy is always quantized, whether treated as a particle in a box or a harmonic oscillator.