oh, so is that the very definition of Hamiltonian , that its eigen vectors are such that their probabilities are unaffected over time ?
Sorry, as I didn't get your question .:blushing:
I might be wrong but,Isn't the Hamiltonian a hermitian operator? So why can't there be eigen vectors for it.
In the example I gave
The hamiltonian is of the form
(
\frac{\partial }{\partial x}
)2 .
So isn't the state vector (corresponding to a definite momentum p),\psi(x) = exp(ipx/ħ) an...
sorry.Perhaps I bungled up and used some wrong terminology.
I will first give an ex.
Consider a free particle moving in 1-D and in absence of any potentials.
thus H = p2/2m , where p is momentum operator.
.
Now consider a \psi (x,t) given by...
Let a state vector \psi is eigen vector for a Hamiltonian H which governs the Schrodinger equation (in its general form)of a system. Then, will probability distribution of \psi w.r.t any observable remain unchanged as time evolves?
Lets say we have a function of a complex variable z , f(z).
I read that for the function to be differentiable at a point z0 , the CR equations are a necessary condition but not a sufficient condition.
Can someone give me an example where the CR equations hold but the function is not...
Call your matrix A and row reduced form matrix rref(A).
rref(A) is obtained by row operations on the original matrix.
Suppose two columns are independent in A, row operations on A can change the span of these two columns , but they will still remain independent.
Thus , the set of columns...
An FBI agent interrogates Sheldon about the character of Howard , as he is about to be given some funding for research by the govt. She asks whether he is a responsible person overall.
And Sheldon incriminates Howard for damaging the plastic retention hub of one of his LOTR blu-ray disk. LOL...
Thanks , the axioms are readily available , so I can look them up.
But I am a bit confused again after the last two posts.:confused:
Probably one more example should clear this.
Lets say we have the set of all ordered pairs ℝxℝ .Can we say that this set in itself is a vector space ?
Or do we...
A vector space is a collection of vectors. So can we say that it is a set (although with special properties) ? Just wanted to confirm this.
Is this also true for a vector space consisting of all functions from R to R , i.e can we say that it is also a set , where each member of the set is a...
there is also another school of thought for what mathematics is. it is Mathematical Formalism.It was advocated by David Hilbert.
There shouldn't be much difference in saying that universe is pure math or pure geometry.
Also I think whether or not universe is pure math or not can be settled...