Number of possible wavefunctions only countably infinite?

[StarsRuler]

this is not true for all cases. for eg., the free particle energy eigenfunctions form a continuous spectrum.
e^{i\frac{\sqrt{2mE}}{\hbar}x}

These functions are not modulus square integrable. His integration in ℝ is ∞

 

[nomadreid]

Physwizard, your wrote:

I see. As per google, rigged has two meanings:
rigged past participle, past tense of rig (Verb)
Verb
1) Make (a sailing ship or boat) ready for sailing by providing it with sails and rigging.
2) Manage or conduct (something) fraudulently so as to produce an advantageous result.
It appears you are interpreting it as per the first meaning, while I was interpreting as per the second which was why I took objection to it.
I do believe mathematical and physical quantities ought to be properly named.

It was named correctly, without ambiguity, in the original Russian (оснащенное гильбертово пространство). Here, this refers to (1), and not to (2). The problem was not in the naming, it is in the problems of translation.

 

[physwizard]

Physwizard, your wrote:It was named correctly, without ambiguity, in the original Russian (оснащенное гильбертово пространство). Here, this refers to (1), and not to (2). The problem was not in the naming, it is in the problems of translation.

oh. didn't know there was a russian angle!