The Hydrogen Atom, Part 1 of 3: Intro to Quantum Physics

Hydrogen Atom

The simplest atom consisting of one proton and one electron, commonly used to illustrate principles of quantum mechanics.

Ground State

The lowest energy state of an atom, where the electron is closest to the nucleus.

Metastable state

An excited state of a system that is stable for a relatively long time but can transition to a lower energy state.

Wave function (Ψ)

A complex-valued function that describes the quantum state of a system, depending on variables such as position and time.

Probability Density

The square of the amplitude of the wave function, providing the likelihood of finding a particle in a given space.

Planck's Constant (h-bar)

A fundamental constant in quantum mechanics, equal to h/(2π), that relates energy and frequency.

Schrödinger equation

An equation that describes how the quantum state of a physical system changes over time, fundamental to quantum mechanics.

Energy Eigenstate

A specific wave function that has a definite energy associated with it, remaining constant in time except for an overall phase factor.

Kinetic Energy Operator (T̂)

An operator in quantum mechanics representing the kinetic energy of a particle, derived from classical formulas.

Potential Energy Operator (V)

An operator representing the potential energy due to a particle's position in a field, such as the Coulomb potential between an electron and a proton.

Hamiltonian Operator (Ĥ)

An operator corresponding to the total energy of a system, combining both kinetic and potential energy.

Laplacian

A second-order differential operator that, in three dimensions, is the sum of the second derivatives with respect to spatial coordinates.

Angular Momentum

A quantity that represents the rotational inertia and rotational motion of a particle; in quantum mechanics, it is quantized.

Spherical Coordinates (R, θ, φ)

A coordinate system used to describe positions in three-dimensional space using a radius and two angles.

Uncertainty Principle

A fundamental principle of quantum mechanics stating that certain pairs of physical properties cannot be simultaneously known to arbitrary precision.

Eigenvalue Problem

A mathematical problem where an operator acts on a function (eigenvector) to produce a multiple of that function (eigenvalue).

Coulomb Potential

The potential energy due to the electrostatic force between charged particles, inversely proportional to the distance between them.

Collapsed State

A state of a quantum system when a measurement is performed, resulting in a definite outcome from a range of probabilities.