Origins of Quantum Physics

The study of matter and energy at the atomic and subatomic level.

A hypothetical object that absorbs all radiation falling on it, making it appear black under reflection. It's a perfect absorber and emitter of radiation.

The continuous distribution of frequencies in electromagnetic radiation emitted by a glowing solid object when heated. It depends only on the temperature of the object, not its composition or shape.

The energy density per unit frequency of blackbody radiation. It describes the energy distribution at different frequencies.

A law stating that the total intensity (power per unit surface area) of radiation emitted by a glowing object is proportional to the fourth power of its temperature. It's expressed as P = σT⁴.

Proposed by Wilhelm Wien in 1894. This formula accurately describes the energy density of blackbody radiation at high frequencies but fails at low frequencies. It's expressed as u(F,T) = AF³e^(-βF/T).

An attempt to explain the continuous character of blackbody radiation by Rayleigh in 1900. It assumes that the energy exchange between radiation and matter is continuous. The law fails at high frequencies, resulting in the ultraviolet catastrophe. It's expressed as u(F,T) = (8πF²/c³)kT.

The failure of classical physics to explain the behavior of blackbody radiation at high frequencies, where predicted energy density diverges to infinity.

The theory proposed by Max Planck in 1900 to explain blackbody radiation. It postulates that the energy exchange between radiation and matter is quantized, occurring in discrete amounts called quanta. This is Planck's quantization rule for energy. It's expressed as E = nhF.

A fundamental constant in quantum mechanics, introduced by Planck, that defines the smallest unit of energy that can be exchanged between radiation and matter. It's approximately 6.626 x 10⁻³⁴ Joule-seconds.

A packet of energy associated with electromagnetic radiation, proposed by Einstein. Its energy is quantized, given by E = hF.

The process of electrons being ejected from a metal surface when irradiated with light.

The minimum frequency of light required to eject electrons from a specific metal. Below this frequency, no electrons are emitted, regardless of the light's intensity.

The minimum energy required to remove an electron from the surface of a metal. It represents the energy an electron must gain to overcome the binding forces holding it to the metal.

An effect where X-rays lose energy when scattered by electrons, which demonstrates the particle nature of light. In this process, the photon interacts with an electron and transfers some of its energy to the electron, resulting in a change in the photon's frequency and wavelength.

A phenomenon predicted by Dirac's equation which states that when light interacts with particles, the energy of a photon can be used to create particle-antiparticle pairs.

A hypothetical wave associated with a material particle, proposed by Louis de Broglie in 1923. Its wavelength is inversely proportional to the particle's momentum: λ = h/p. It demonstrates the wave-like behavior of matter at the microscopic level.

The experimental confirmation of the wave-like properties of matter. Davisson and Germer in 1927 observed interference patterns, a characteristic of waves, when electrons were diffracted by a crystal.

This principle implies that any physical system, like an electron or a photon, can exist in a superposition of multiple states, each with a specific probability. This means a particle doesn't have a definite position or momentum, but rather exists in a mixture of possibilities until measured.

Introduced by Werner Heisenberg in 1927, it states that the more precisely one knows the position of a quantum particle, the less precisely one can know its momentum and vice versa. The product of the uncertainties in position and momentum must be greater than or equal to Planck's constant divided by 4π: ΔxΔp ≥ h/4π.

The interpretation of the wave function in quantum mechanics, proposed by Max Born in 1927. It states that the square modulus of the wave function gives the probability density of finding a particle at a particular point in space and time.

The first formulation of Quantum Mechanics developed by Werner Heisenberg in 1925, to describe atomic structure based on observed spectral lines. It uses matrices to represent physical quantities and treats the dynamics of microscopic systems as an eigenvalue problem.

The second formulation of Quantum Mechanics developed by Erwin Schrödinger in 1926, which generalizes the de Broglie postulate. It describes the dynamics of microscopic systems by means of a wave equation, the Schrödinger equation.

A mathematical relation that describes the time evolution of a quantum system. It's a fundamental equation in quantum mechanics and comes in two forms: time-independent and time-dependent.

A specific solution to the Schrödinger equation for a given potential, representing a state with a definite energy and unchanging in time. This state is characterized by a constant energy and a wave function that is independent of time.

The process of an atom transitioning between energy levels, accompanied by the absorption or emission of photons.

A set of sharp, colored lines in the spectrum of light emitted by excited atoms. Each line corresponds to a specific energy transition between energy levels in the atom.

A model of the atom proposed by Ernest Rutherford in 1911. It describes the atom as a positively charged nucleus surrounded by negatively charged electrons orbiting it.

A model of the hydrogen atom proposed by Niels Bohr in 1913, which combines Rutherford's model with Planck's quantum concept and Einstein's photons. It postulates that atoms can only exist in discrete states of energy and that electron transitions between these states result in the absorption or emission of photons.

The wave functions that describe the behavior of a particle in a specific quantum state, where the square of the wave function's amplitude is interpreted as the probability density of finding the particle at a certain point in space and time. It's a solution to the Schrödinger equation.

A representation scheme in quantum mechanics devised by Paul Dirac that simplifies the description of states and operators using bra and ket notation. It simplifies the mathematical representation of quantum states and operators, making them more compact and easier to manipulate.

A mathematical object that acts on a state (wave function) to transform it. In quantum mechanics, operators represent measurable quantities such as position, momentum, energy, and angular momentum. They are used to describe the physical observables of a system.

A mathematical relation that defines how two operators act upon each other. The commutator of two operators tells us whether they can be measured simultaneously and what the uncertainty in their measurement will be. It's represented as [A,B] = AB - BA.

A set of commuting operators that completely describe a quantum system. The eigenvalues of a complete set of commuting operators provide a complete set of quantum numbers for the system, specifying its state uniquely.

A mathematical tool for describing the evolution of a quantum system over time. It's an operator that acts on the state vector at a given time to determine the state at a later time. It's expressed as U(t) = exp(-iHt/ħ).

The concept in quantum mechanics that all possible states of a system can be represented as a linear combination of a set of basis states. The basis states form a complete set, meaning that any other state can be expressed as a weighted sum of the basis states.

The study of the behavior of quantum particles interacting with potential energy fields. It utilizes the Schrödinger equation to predict the particle's behavior in different potential scenarios.

A region where a particle is confined. The potential energy changes abruptly, creating boundaries for the particle's movement.

A phenomenon where a particle has a non-zero probability of penetrating a potential barrier, even if its energy is less than the barrier height. This is a purely quantum mechanical effect, impossible in classical physics.

A fundamental property of quantum systems that describes the total angular momentum of a particle. It can be orbital (due to the particle's motion) and spin (an intrinsic property of the particle). It's quantized, meaning it only takes on specific discrete values.

The part of angular momentum that arises from the motion of a particle around a central axis. It's quantized and is represented as a vector quantity, with magnitude and direction.

The intrinsic angular momentum of a particle, which is an inherent property of the particle itself, like its mass or charge. This property doesn't depend on the particle's motion. It's quantized and is represented as a vector quantity.

A fundamental particle property that arises from the fact that electrons act as both a wave and a particle, possessing an intrinsic angular momentum. It's quantized, taking on values of h/4π. It's responsible for magnetism, due to the spinning charged particle.

The study of quantum systems in three dimensions, where the Schrödinger equation is solved using spherical coordinates to describe particles in spherical potential fields, such as atoms.

A type of potential energy field in which the potential energy depends only on the distance from a central point, like the force of gravity. It's often used to describe atoms, where electrons move around a central nucleus.

The fundamental building block of all atoms, consisting of a positively charged nucleus surrounded by negatively charged electrons. It's the simplest atom, with one proton and one electron.

A method for solving the Schrödinger equation, where we break down the problem into smaller, simpler parts. Each part is solved separately, and then the solutions are combined to obtain the complete solution.

A theoretical method that allows us to study the behavior of a quantum system under the influence of a small perturbation, or change, applied to the system. It's used to calculate changes in energy levels and properties of a system when it's slightly disturbed.

A method for finding approximate solutions to the Schrödinger equation. It relies on minimizing the energy of the system to obtain the best possible approximation for its ground state.