Atomic orbitals can be the hydrogen-like " orbitals " which are exact solutions to the Schrödinger equation for a hydrogen-like " atom " ( i. e., an atom with one electron ).

With de Broglie's suggestion of the existence of electron matter waves in 1924, and for a short time before the full 1926 Schrödinger equation treatment of hydrogen like atom, a Bohr electron " wavelength " could be seen to be a function of its momentum, and thus a Bohr orbiting electron was seen to orbit in a circle at a multiple of its half-wavelength ( this historically incorrect Bohr model is still occasionally taught to students ).

In the Schrödinger equation for this system of one negative and one positive particle, the atomic orbitals are the eigenstates of the Hamiltonian operator for the energy.

Dirac realised that his relativistic version of the Schrödinger wave equation for electrons predicted the possibility of antielectrons.

* Solutions to the radial Schrödinger equation ( in spherical and cylindrical coordinates ) for a free particle

Swiss physicist Felix Bloch provided a wave function solution to the Schrödinger equation with a periodic potential, called the Bloch wave.

For example, most ab initio calculations make the Born – Oppenheimer approximation, which greatly simplifies the underlying Schrödinger equation by assuming that the nuclei remain in place during the calculation.

Computational chemists often attempt to solve the non-relativistic Schrödinger equation, with relativistic corrections added, although some progress has been made in solving the fully relativistic Dirac equation.

In principle, it is possible to solve the Schrödinger equation in either its time-dependent or time-independent form, as appropriate for the problem in hand ; in practice, this is not possible except for very small systems.

The total energy is determined by approximate solutions of the time-dependent Schrödinger equation, usually with no relativistic terms included, and by making use of the Born – Oppenheimer approximation, which allows for the separation of electronic and nuclear motions, thereby simplifying the Schrödinger equation.

The programs used in computational chemistry are based on many different quantum-chemical methods that solve the molecular Schrödinger equation associated with the molecular Hamiltonian.

As these methods are pushed to the limit, they approach the exact solution of the non-relativistic Schrödinger equation.

Once the electronic and nuclear variables are separated ( within the Born – Oppenheimer representation ), in the time-dependent approach, the wave packet corresponding to the nuclear degrees of freedom is propagated via the time evolution operator ( physics ) associated to the time-dependent Schrödinger equation ( for the full molecular Hamiltonian ).

In the complementary energy-dependent approach, the time-independent Schrödinger equation is solved using the scattering theory formalism.

Lieb and Yau have given a rigorous derivation of the limit from a relativistic many-particle Schrödinger equation.

Provided the theory is linear with respect to the wavefunction, the exact form of the quantum dynamics modelled, be it the non-relativistic Schrödinger equation, relativistic quantum field theory or some form of quantum gravity or string theory, does not alter the validity of MWI since MWI is a metatheory applicable to all linear quantum theories, and there is no experimental evidence for any non-linearity of the wavefunction in physics.

On the other hand the Bohm interpretation of quantum mechanics keeps counter-factual definiteness while introducing a conjectured non-local mechanism in form of the ' quantum potential ', defined as one of the terms of the Schrödinger equation.

The Dyson series, the formal solution of an explicitly time-dependent Schrödinger equation by iteration, and the corresponding Dyson time-ordering operator an entity of basic importance in the mathematical formulation of quantum mechanics, are also named after Dyson.

Within the framework of the approach a theory was proposed in which the physical vacuum is conjectured to be the quantum Bose liquid whose ground-state wavefunction is described by the logarithmic Schrödinger equation.

* solutions of the Schrödinger wave equation

For example, as the only neutral atom with an analytic solution to the Schrödinger equation, the study of the energetics and bonding of the hydrogen atom played a key role in the development of quantum mechanics.

Similar to an atomic orbital, a Schrödinger equation, which describes the behavior of an electron, can be constructed for a molecular orbital as well.

To further illustrate, Schrödinger describes how one could, in principle, transpose the superposition of an atom to large-scale systems.

The Schrödinger equation describes the wave-like behavior of particles in quantum mechanics.

Although it is not a successful relativistic generalization of the Schrödinger equation, this equation is resurrected in the context of quantum field theory, where it is known as the Klein – Gordon equation, and describes a spinless particle field ( e. g. pi meson ).

In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of a physical system changes with time.

Also like Newton's Second law, the Schrödinger equation describes time in a way that is inconvenient for relativistic theories, a problem that is not as severe in matrix mechanics and completely absent in the path integral formulation.

The Schrödinger equation describes the ( deterministic ) evolution of the wavefunction of a particle.

Just as the Schrödinger equation describes how pure states evolve in time, the von Neumann equation ( also known as Liouville-von Neumann equation ) describes how a density operator evolves in time ( in fact, the two equations are equivalent, in the sense that either can be derived from the other.

In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic.

The Schrödinger wave equation describes energy eigenstates having corresponding real numbers E < sub > n </ sub > with a definite total energy which the value of E < sub > n </ sub > defines.

Unlike the Schrödinger equation, it never describes the time evolution of a quantum state.

In quantum mechanics, it is a special case of the nonlinear Schrödinger field, and when canonically quantized, it describes bosonic point particles with delta-function interactions — the particles either repel or attract when they are at the same point.

File: Schrodinger. jpg | Erwin Schrödinger ( 1887-1961 ): formulated the Schrödinger equation in 1926 describing how the quantum state of a physical system changes with time, awarded the Nobel Prize in Physics in 1933, two years later proposed the thought experiment known as Schrödinger's cat

The Schrödinger equation provides a way to calculate the possible wavefunctions of a system and how they dynamically change in time.

The laws of quantum mechanics ( the Schrödinger equation ) describe how the wave function evolves over time.

However, no-one, even Schrödinger and De Broglie, were clear on how to interpret it.

The process of quantum decoherence explains in terms of the Schrödinger equation how certain components of the universal wave function become irreversibly dynamically independent of one another ( separate worlds – even though there is but one quantum world that does not split ).

In 1926, Erwin Schrödinger published an equation describing how this matter wave should evolve — the matter wave equivalent of Maxwell ’ s equations — and used it to derive the energy spectrum of hydrogen.

The Schrödinger wave equation, describing states of quantum particles, has solutions that describe a system and determine precisely how the state changes with time.

It tells how the probability distribution function evolves in time similarly to how the Schrödinger equation gives the time evolution of the quantum wave function or the diffusion equation gives the time evolution of chemical concentration.

In 1972 H. Hasimoto used Da Rios ' " intrinsic equations " ( later re-discovered independently by R. Betchov ) to show how the motion of a vortex filament under LIA could be related to the non-linear Schrödinger equation.

coined the term in 1983 as an analogy to how organisms survive by consuming negative entropy ( as suggested by Erwin Schrödinger