Ambition On Acid

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To cut a long story short, as they say , I'm throwing together a kind of "pub quiz" for some friends - it's maths based. The idea is you have to find sums for certain numbers but you're not allowed to use some basic maths operations. Now I just need clarification on something: If you weren't allowed to use subtraction when you're coming up with sums would you still be allowed to use negative numbers? (e.g. -4 + 5) I've never been sure whether, when you do a simple sum like "5 -3" you're doing "+5 - +3" or what you're actually doing is "+5 -3" I've never been sure because you can do sums like " -5 - -3" as well Clarification appreciated!

I have just a simple question about the imaginary number i : Since it's the square root of -1, is -i2 equal to 1? Thanks

As I said: layman terms.

So to put this into simple, layman terms : A pure state is ONE wavefunction, (Ψ) while a mixed state is several ensemble 'wavefunctions.' (?)

So is it possible for a wavefunction to have a entropy higher than zero?

So this pure state your referring to is just the wavefunction?

Okay, but if we were to treat the microstates like macrostates would each one (hypothetically) have independent entropy values?

Hello everyone. I have two questions, that I've been turning over in my head, I hope some one can clarify. The first one: When a particle (or some other quantum system) is in an uncollapsed superposition of states, do each of these states, when considered individually, have different (assumably very small) entropy values to one another? The second (unrelated) one: When the probability amplitudes of a wavefunction are normalised, must the sum always equal 1? Thanks!