What is the reason the commutation relation fails on the last state
N=7
M=6
commutator(position(N),momentum(N))*basis(N,M)==1.0j*basis(N,M)
and similarly for the create and destroy commutator?
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Francois Vanderseypen
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Because you are in a truncated Hilbert space, and your excitation is in the upmost level. Thus a creation operator promotes you out of the Hilbert space.
Paul Nation
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Would an exception be not more appropriate in that case? This behavior leads to issues/bugs in a large application. The documentation is really not clear about this truncation in any case. – Francois Vanderseypen Jan 25 '17 at 05:46
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What would you do? The oscillator formally lives in an infinite dimensional Hilbert space that one must truncate at some level. The error is an indication that you need more basis states for the level of excitation in your system. This error can actually be used to check if enough basis states are included. – Paul Nation Jan 25 '17 at 05:51