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Tagged with normalizationhomework-and-exercises
53 questions
1vote
1answer
106views
Question on the square-integrability of the given wavefunction at origin and infinity
I have this function as a wavefunction of a quantum system: $$\psi(r)=N r^a \exp\left(br^2 + cr+\frac d{r^3}+\frac e{r^2}+\frac f{r}\right)$$ where $r$ is the radial parameter ranging on the interval $...
- 13
1vote
1answer
173views
What happens to the normalization condition if the wave function is non stationary?
The quantum mechanics courses I have taken as of now pretty much only deal with stationary states of the form: $$\psi(x,t) = \psi(x)\exp{\left(-\frac{iE}{\hbar}t\right)} $$ Now, what about situations ...
- 4,081
-1votes
1answer
130views
Normalize the wave function with spherical harmonics [closed]
I have this wave function: $$\Psi=C e^{-\rho / 2} \rho^{l} L_{1}^{3} Y_{l, m} $$ To normalize the function I have tried to express the polynomial in the function as follows. If: $$L_{1}^{3}(x)=(-1)^{1}...
- 23
0votes
1answer
136views
Normalising a free particle wave function, at $t=0$
I am trying to normalise the wave function $\psi$ for a free particle, with initial boundary conditions. $$\Psi(x,0)=Ae^{-2|x|}.$$ When trying to normalise it, I keep getting $\infty$ which clearly ...
-1votes
1answer
74views
Showing that a wavefunction in column form is normalised [closed]
I am given the following wavefunction in column form: $\psi = \begin{bmatrix} \frac{1}{4} \\ \sqrt{\frac{15}{16}}i \end{bmatrix} $ And asked to show that it is normalised. As I understand it, the ...
- 169
0votes
2answers
87views
Eigenfunction of wave vector [closed]
I am reading some book, where it is said that the eigenfunctions are given by $$\langle \mathbf{r}|\mathbf{k}\rangle = \frac{1}{\sqrt{\Omega}} \mathrm{e}^{i \mathbf{k} \cdot {\mathbf{r}}}$$ First of ...
1vote
2answers
6kviews
How do I normalise the wavefunction of a hydrogen 1s orbital to obtain the normalisation constant?
The wavefunction I've been given for a 1s hydrogen orbital is: $$ \Psi = A e^{-r} $$ And I need to normalize this to find the value of A. I understand to normalise this I would inset this wave ...
- 25
2votes
1answer
260views
$\int_{-\infty}^{\infty} |\psi(x)|^2 ~ dx = 1$ when $\psi(x) = C\exp\left(\frac{x^2}{2a^2} + \frac{ix^3}{3a^3}\right)$ [closed]
The information given is: Consider a state $|\psi\rangle $ describing a quantum particle on a line, whose position representation $\langle x|\psi\rangle = \psi(x)$ is given by: \begin{gather*} \...
user289943
1vote
0answers
278views
How to find probability of finding a particle outside the region in which it is confined?
Problem: Consider a one-dimensional particle of mass $m$ which is confined within the region $0 \le x \le a$ by a potential $V(x)$ and whose wave function is $\Psi(x, t) = \sin(\pi x/a)\exp(−i\omega t)...
- 11
3votes
2answers
582views
How do I prove that an electron beam has a plane wave function?
I have been told that an electron beam has a wave function equivalent to a plane wave $\psi(x) = Ae^{ikx}$, however I would like to know why? Also, if an electron beam can be shown to have a wave ...
- 75
4votes
2answers
3kviews
How to Normalize a Wave Function?
To talk about this topic let's use a concrete example: Suppose I have a one-dimensional system subjected to a linear potential, such as the hamiltonian of the system is: $$H=\frac{\hat{p}^2}{2m}-F\hat{...
- 4,683
1vote
1answer
1kviews
Two non-interacting particles in a 1D box
I need to find the wave function for two non-interacting particles of mass $m_1$ and $m_2$ in 1D infinite box (well) of length $L$, where the positions of the particle is given by $x_i$ ($i$ being $1,...
- 1,481
0votes
0answers
82views
Wave functions without normalization
I'm working on a problem where we find the probability of finding a particle between $a/4$, and $3a/4$. The particle is confined between $0$ and $a$. Normally I would attack this by normalising the ...
- 71
-2votes
2answers
458views
How can you calculate the normalisation factor? [closed]
when given a particle of mass $m$ in a one dimensional square potential well from $x=0-L$, How can one calculate the value of the normalisation factor $|φ\rangle = |A|(\,|1\rangle + |2\rangle\,)$ ...
1vote
1answer
4kviews
Normalization of a Wave-function in spherical co-ordinates [closed]
So I have been provided with the following wave-function $ψ(x, y, z) = N(x + y + z)e^\frac{ −r^ 2}{α^2}$ I am trying to convert it to spherical co-ordinates and to find the Normalization constant $N$...
