What is "function of period unity"?
Hi,
I'm reading an article that has a sentence saying "where P is a function of period unity.".
Here.
I've been looking for what does it mean but without any success. Does anyone know?
It got a bit messy, so let me explain. When you write f(x) ##\in ## R, it means f(x) is real number, i.e. the output from the function is a number. But when you write f(x) ##\in ## P(R), it means f(x) takes values in P(x), meaning output of f is element of P(R), meaning output of f is a subset...
Correct way to write it is f(x) ##\in ## P(R). If you think about it a little bit more, you will surely understand it very clearly. Read article on wikipedia about power sets, if you need.
You almost got it;)
The answer lies in the expression
f(x) = {y ∈ R; sin y < x}.
If it was...
Pretty much. More correct way to think about it is that f assigns to each x a subset of R, therefore f(x) is equal to a single element of P(R).
The important concept here is that set can be taken as element of other set.
Exactly. To decide between 3 and 5, notice the strict inequality in...
What happens when you take power set of some set is that each subset is taken as element of P(S), where S is arbitrary set. For example, power set of S = {1, 2, 3} is {{1}, {2}, {3}, {1, 3}, {2, 3}, {1, 2, 3}}. So function from, say, R to P(x) assigns to each real number a subset of that set...
P(R) probably means power set of real numbers, meaning to each real number x it assigns a subset of real numbers. You can imagine that for each number x it assigns a set of numbers, such that sin y < x. You can imagine a plot of sine with horizontal line located at height x, and the f(x) would...
So, if I understand it correctly, if we have time-indep potential we can use time-indep Schrödinger equation(=eigenvalue problem for Hamiltonian) to derive set of solutions for t=0, from which any other state can be formed(=they form orthonormal basis) and which can be developed into any later...
You are right, I missed this subtlety.
There is also a nice article on wiki on wavefunction collapse. Some interpretations apparently doesn't require a collapse.