@Zalgo n the mathematically rigorous formulation of quantum mechanics developed by Paul Dirac,[17] David Hilbert,[18] John von Neumann,[19] and Hermann Weyl,[20] the possible states of a quantum mechanical system are symbolized[21] as unit vectors (called state vectors). Formally, these reside in a complex separable Hilbert space—variously called the state space or the associated Hilbert space of the system—that is well defined up to a complex number of norm 1 (the phase factor). In other words, the possible states are points in the projective space of a Hilbert space, usually called the co…

@Zalgo In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wave function, also referred to as state vector in a complex vector space.[22] This abstract mathematical object allows for the calculation of probabilities of outcomes of concrete experiments. For example, it allows one to compute the probability of finding an electron in a particular region around the nucleus at a particular time. Contrary to classical mechanics, one can never make simultaneous predictions of conjugate variables, such as position and momentum, to arbitrary precisi…

@Zalgo In the everyday world, it is natural and intuitive to think of everything (every observable) as being in an eigenstate. Everything appears to have a definite position, a definite momentum, a definite energy, and a definite time of occurrence. However, quantum mechanics does not pinpoint the exact values of a particle's position and momentum (since they are conjugate pairs) or its energy and time (since they too are conjugate pairs); rather, it provides only a range of probabilities in which that particle might be given its momentum and momentum probability. Therefore, it is helpful t…

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Quantum mechanics
From Wikipedia, the free encyclopedia
Not to be confused with Quantum field theory.
For a more accessible and less technical introduction to this topic, see Introduction to quantum mechanics.
Solution to Schrödinger's equation for the hydrogen atom at different energy levels. The brighter areas represent a higher probability of finding an electron.
Quantum mechanics
H ^ | ψ ( t ) ⟩ = i ℏ ∂ ∂ t | ψ ( t ) ⟩ {\displaystyle {\hat {H}}|\psi (t)\rangle =i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle } {\displaystyle {\ha…