Linked Questions

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0answers
27 views

Finite square well and continuity [duplicate]

In solving finite square well problem, we solve the TISE inside and outside the well, and we match the wave function at the boundary, by the continuity of wave function. Now this bugs me, since the ...
21
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3answers
6k views

Smoothness constraint of wave function

Is there anything in the physics that enforces the wave function to be $C^2$? Are weak solutions to the Schroedinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't ...
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2answers
6k views

Expectation value of Hamiltonian?

Consider a particle in an infinite potential well with length $L$: $\forall x \in (0,L): V(x) = 0$ and $V(x) = \infty$ elsewhere. The wave function at time $t = 0$ is given by $$ \psi(x,0) = \begin{...
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3answers
1k views

Particle in a box: value for wave function $u(x)$ when potential $V(x)$ is infinity

The time-independent Schrödinger equation (TISE) is: $$ -\frac{\hbar^2}{2m}\frac{d^2 u(x)}{dx^2}+V(x)u(x)=Eu(x) \hspace{15pt}$$ where $E$ is a constant. Imagine now a infinity potential well as ...
1
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3answers
6k views

Why is $ \psi = A \cos(kx) $ not an acceptable wave function for a particle in a box?

Why is $ \psi = A \cos(kx) $ not an acceptable wave function for a particle in a box with rigid walls at $x=0$ and $x=L$ where $$ k = \frac {(2mE)^{1/2}} {\hbar} \, ?$$ I had plugged the wave ...
3
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1answer
2k views

Bohr-Sommerfeld quantization for different potentials

Let's have Bohr-Sommerfeld quantization for one-dimensional case: $$ \int \limits_{a}^{b} p(x)dx ~=~ \pi \hbar (n + \nu ). $$ Here $p(x) = \sqrt{2m(E - U)}$, $a, b$ are turning points, and the area ...
1
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1answer
705 views

(Level: Undergrad) Continuity Conditions on the Wavefunction and Initial Values

I know that a physically meaningful $\Psi$ needs to be continuous. However, recently I came across a problem in which they were considering a wavefunction for the infinite square well potential and ...
1
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2answers
584 views

Particle in a one dimensional box conditions

Why does the wave function have to be $C^1(\mathbb{R})$ for a finite square well but not for an infinite square well? For an infinite square well with boundaries at $x=0$ and $x=L$, we have $$\psi_n(x)...
4
votes
2answers
327 views

Rectangular window $\psi$ wave-function and the calculus of $\langle p^2\rangle$ for it

I'm currently considering a rectangular window $\psi$ function: $$ \psi(x) = \begin{cases}\left(2a\right)^{-1/2}&\text{for } |x|<a \\ 0&\text{otherwise.} \end{cases} $$ I am interested in ...
5
votes
1answer
660 views

Does the wavefunction need to be continuous and satisfy other boundary conditions?

So, please don't ignore this question thinking it's a duplicate or something. I have read all the answers on StackExchange and in other articles, but either the math is too confusing, or the answers ...
0
votes
2answers
420 views

What would be required to get a discontinuous solution of the Schrödinger equation?

I'm thinking about the possibility of a discontinuous solution of the Schrödinger equation and what is needed to get such an object. It should be a condition to the potential, I think. If the ...
-1
votes
2answers
254 views

Discontinuous derivative of wavefunctions in the infinite square well potential problem?

I am intrigued about two points given in an answer to a similar question (https://physics.stackexchange.com/a/38198/262985). On one hand, it is stated that wavefunctions inside the well (excluding ...