Komt er op neer dat je de eigenstaat van bijvoorbeeld een atoom gaat bepalen. Stel je wil een electron naar een hogere schil jagen. Op dat moment verander je de eigenstaat van dat atoom. De eigenstaat is de de huidige toestand waar dat atoom zich in bevindt. Nu is dankzij het onzekerheidsprincipe die toestand niet vast bepaald. Ken je het moment dan is de plaats van dat electron niet bepaald. Dan kan je dus onmogelijk zeggen dat het electron zich op een welbepaalde plaats bevindt. Niet omdat we het niet kunnen vinden maar omdat het overal kan zijn.
http://en.wikipedia.org/wiki/Introducti ... igenstates
Because of the uncertainty principle, statements about both the position and momentum of particles can only assign a probability that the position or momentum will have some numerical value. The uncertainty principle also says that eliminating uncertainty about position maximises uncertainty about momentum, and eliminating uncertainty about momentum maximizes uncertainty about position. A probability distribution assigns probabilities to all possible values of position and momentum. Schrödinger's wave equation gives wavefunction solutions, the squares of which are probabilities of where the electron might be, just as Heisenberg's probability distribution does.[1][2][3]
In the everyday world, it is natural and intuitive to think of every object being in its own eigenstate. This is another way of saying that every object appears to have a definite position, a definite momentum, a definite measured value, and a definite time of occurrence. However, the uncertainty principle says that it is impossible to measure the exact value for the momentum of a particle like an electron, given that its position has been determined at a given instant. Likewise, it is impossible to determine the exact location of that particle once its momentum has been measured at a particular instant.[1]
Therefore it became necessary to formulate clearly the difference between the state of something that is uncertain in the way just described, such as an electron in a probability cloud, and the state of something having a definite value. When an object can definitely be "pinned down" in some respect, it is said to possess an eigenstate. As stated above, when the wavefunction collapses because the position of an electron has been determined, the electron's state becomes an "eigenstate of position", meaning that its position has a known value, an eigenvalue of the eigenstate of position.[4]
The word "eigenstate" is derived from the German/Dutch word "eigen", meaning "inherent" or "characteristic". An eigenstate is the measured state of some object possessing quantifiable characteristics such as position, momentum, etc. The state being measured and described must be observable (i.e. something such as position or momentum that can be experimentally measured either directly or indirectly), and must have a definite value, called an eigenvalue. ("Eigenvalue" also refers to a mathematical property of square matrices, a usage pioneered by the mathematician David Hilbert in 1904. Such matrices are called self-adjoint operators, and represent observables in quantum mechanics[5])
De eigenwaarden die vast hangen aan die eigenstaat kan worden voorgesteld door een wiskundige matrix.
Even verduidelijken. Die eigenwaarden zijn alle mogelijke waarden van een eigenstaat die men kan voorstellen in een matrix. Hoewel een eigenstaat verschillende mogelijke eigenwaardes kan hebben zijn die wel discreet bepaald. Het zijn die waardes uit de matrix, niet tussen die en die waarde, enkel en alleen die waarden.
De wiskunde komt dus inderdaad van de statistiek die jij gebruikt. En idd het is per definitie geen zwart wit ding omdat het over probabiliteit gaat. De kansverdeling waar dat electron zich kan bevinden als je het moment kent (of omgekeerd).
Meer uitleg:
http://en.wikipedia.org/wiki/Quantum_state
In the mathematical formulation of quantum mechanics, pure quantum states correspond to vectors in a Hilbert space, while each observable quantity (such as the energy or momentum of a particle) is associated with a mathematical operator. The operator serves as a linear function which acts on the states of the system. The eigenvalues of the operator correspond to the possible values of the observable, i.e. it is possible to observe a particle with a momentum of 1 kg⋅m/s if and only if one of the eigenvalues of the momentum operator is 1 kg⋅m/s. The corresponding eigenvector (which physicists call an "eigenstate") with eigenvalue 1 kg⋅m/s would be a quantum state with a definite, well-defined value of momentum of 1 kg⋅m/s, with no quantum uncertainty. If its momentum were measured, the result is guaranteed to be 1 kg⋅m/s.
