[kevyk]

[ QUOTE ]
No efficient program would calculate values until they are needed.[it must be best to work this way as most of the time the value is never measured]


[/ QUOTE ]

This is pretty much how the the equations of QM work. A particle's quantum state is represented by a probability density function (psi) in either position or momentum space. Psi can be represented as a vector in an infinite-dimensional Hilbert space, because all psi's are orthogonal to each other. "Measurements" are represented in this theoretical framework by non-commuting operators which return an eigenstate of psi. The fact that the operators don't commute (meaning that first operating on psi with the position operator, then with the momentum operator gives different results than the reverse) is in some sense the guts of QM.

Most interesting problems in QM involve particles or systems of particles which are in a superposition of quantum states, where psi = a*psi1 + b*psi2 + ..., in which case the probability of measuring the particle to be in state psi1 is a^2/(a+b+...)^2.

Where I think you go wrong is in saying that there's something deterministic going on in the measurement process. While you could be right, there's no evidence to support this, and QM works just fine without it.

You sound like you know probability and linear algebra pretty well--a book in introductory QM might be acessible to you. H.J. Griffiths has written a pretty good one.