Homework Statement
Determine for what k f(x)=xk is an element of L2 (0,1) vector space
k ∈ ℝ
Homework EquationsThe Attempt at a Solution
\int_{0}^{1} x^{2k} dx = \frac{1-0^{2k+1}}{1+2k} = \sum_{n=0}^{\infty}{(-2k)^{n}} (for k > -½)
This sum should converge for
\lim_{n \to +\infty}...
Here is the problem, and how Psi(x,0), Psi(x,t), and Phi(k) are constructed
Now I have found parts A-C fine, with
\Psi(x,0) having a normalization constant of
\sqrt{\frac{a}{2\pi}} \\
\phi(k) = \frac{2a}{k^2+a^2}\sqrt{\frac{a}{2\pi}}
For the last part, I understand how for small a Psi has...
Yeah I can do that in a few hours. I'm not sure how to use latex so I'll have to look that up since I don't see a way to graphically insert symbols.
In the meantime, this is the text in the book the problem refers to. It's from an older edition on my phone which doesn't have the practice...
Homework Statement
Griffiths Intro Quantum Mechanics free particle question.
Normalize wave function, find Phi(k), Psi(x,t), and comment on its behavior for small and large a.
The wave function given is Ae-a|x|Homework EquationsThe Attempt at a Solution
I found the correct Phi(k), but for the...
This lemma the book states, I can't make sense of it.
Lemma: If a,b\in Z and b > 0, there exist q,r \in Z such that a = qb + r with 0 \leq r < b.
Proof: Consider the set of all integers of the form a-xb with x \in Z. This set includes positive elements. Let r = a - qb be the least...
Thanks
I am in the US, but considering going out of country for graduate school.
Were you able to find research even after receiving your BA? Was it at the same university you attended or a different one? I am worried research positions would be filled by undergrad students only.
Also, I...
I switched majors after my third year to physics. As a result, I have an unordinary schedule. I will be graduating either in summer of 2015 or fall of 2015. I haven't taken the GREs yet, and I am not planning on taking them this coming fall since I am doubling up on physics courses and don't...