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.
An important aspect of quantum mechanics is the quantization of many observable quantities of interest. In particular, this leads to quantum numbers that take values in discrete sets of integers or half-integers; although they could approach infinity in some cases. This distinguishes quantum mechanics from classical mechanics where the values that characterize the system such as mass, charge, or momentum, all range continuously. Quantum numbers often describe specifically the energy levels of electrons in atoms, but other possibilities include angular momentum, spin, etc. An important family is flavour quantum numbers – internal quantum numbers which determine the type of a particle and its interactions with other particles through the fundamental forces. Any quantum system can have one or more quantum numbers; it is thus difficult to list all possible quantum numbers.
Quantum system
The tally of quantum numbers varies from system to system and has no universal answer. Hence these parameters must be found for each system to be analyzed. A quantized system requires at least one quantum number. The dynamics (i.e. time evolution) of any quantum system are described by a quantum operator in the form of a Hamiltonian, H. There is one quantum number of the system corresponding to the system's energy; i.e., one of the eigenvalues of the Hamiltonian. There is also one quantum number for each linearly independent operator O that commutes with the Hamiltonian. A complete set of commuting observables (CSCO) that commute with the Hamiltonian characterizes the system with all its quantum numbers.
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Le cours comporte deux parties. Les bases de la thermodynamique des équilibres et de la cinétique des réactions sont introduites dans l'une d'elles. Les premières notions de chimie quantique sur les é
In physics, the spin quantum number is a quantum number (designated s) that describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. It has the same value for all particles of the same type, such as s = 1/2 for all electrons. It is an integer for all bosons, such as photons, and a half-odd-integer for all fermions, such as electrons and protons. The component of the spin along a specified axis is given by the spin magnetic quantum number, conventionally written ms.
In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a quantum mechanical prediction for the system represented by the state. Knowledge of the quantum state together with the quantum mechanical rules for the system's evolution in time exhausts all that can be known about a quantum system. Quantum states may be defined in different ways for different kinds of systems or problems.
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.
Simulating the dynamics of large quantum systems is a formidable yet vital pursuit for obtaining a deeper understanding of quantum mechanical phenomena. While quantum computers hold great promise for speeding up such simulations, their practical applicatio ...
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Quantum optics studies how photons interact with other forms of matter, the understanding of which was crucial for the development of quantum mechanics as a whole. Starting from the photoelectric effect, the quantum property of light has led to the develop ...
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This work presents a recommendation system for metal-organic frameworks (MOFs) inspired by online content platforms. By leveraging the unsupervised Doc2Vec model trained on document-structured intrinsic MOF characteristics, the model embeds MOFs into a hig ...