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By Breit G.

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Therefore the density matrix representing the sub-ensemble of systems which have given result λj is f wk ψk |Pj |ψk ρj := k Pj |ψk ψk |Pj , ||Pj |ψk ||2 for some factor f . Since ||Pj |ψk ||2 = ψk |Pj |ψk , this can be written as wk |ψk ψk |)Pj = f Pj ρPj , ρj := f Pj ( k 14 Note that the operator [A, B] is in general not Hermitian. However we can still define the ‘expectation value’ as [A, B] ψ := | ψ|[A, B]|ψ |. © 2008 by Taylor & Francis Group, LLC Quantum Mechanics 25 and f = [Tr(Pj ρPj )]−1 so that Tr(ρj ) = 1.

If there is more than one charge the term Vcoul is added to the energy. This scheme can be modified by adding a further external control electric field possibly time varying which modifies the shape of the well, for example by placing the system in a capacitor. 34) with the control field playing the Ex . , [200]). Some analysis on the effect of an external field on the motion of a single electron in a quantum well is given in [154]. 2 Canonical quantization Canonical quantization is the process which associates quantities in classical mechanics with operators in quantum mechanics.

This scheme may represent a particle with negative charge such as an electron confined between two negatively charged plates. The system is also referred to as a particle in a box. Classically, in the absence of friction and viscous forces, the particle moves back and forth between the two walls of a box. To describe the system in quantum mechanics, we choose a Hilbert space spanned by the position eigenvectors {|x } so that the state |ψ can be written as |ψ(t) := R I ψ(x, t)|x dx, with ψ(x, t).

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An Interpretation of Diracs Theory of the Electron by Breit G.

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