Schrodinger equation Definition and 549 Threads

Hi, it's been so long since I learned quantum mechanics. So the only thing I can solve now is the square quantum well problem. But I need help because I have to solve this problem of quantum well. I tried some calculation but not far.I try to draw the capacitance-voltage profile by drawing the...

C is just the constant by ##\psi''## My initial attempt was to write out the schrodinger equation in the case that x>0 and x<0, so that $$ \frac {\psi'' (x)} {\psi (x)} = C(E-V(x))$$ and $$ \frac {\psi'' (-x)} {\psi (-x)} = C(E-V(-x))$$ And since V(-x) = V(x) I equated them and...

I've got the solution to the question but I just need more detail. I can't work out the first step of the solution to the second step. That should read, I don't know what they multiplied ih-bar by to make it (i/h-bar)^2?

i have an exam in 2 days and in this question i don't know how should i proceed after that i simplified the wave function but i don't know how to confirm that it's an eigenfunction

I would like to discuss the Schrödinger equation in order to get some insight. The equation, as I understand it, is essentially an expression of the conservation of energy. What it says is that ∆Total Energy= ∆ Kinetic Energy + ∆ Potential Energy. In Schrödinger's day, there were various...

Hello, I am trying to find the solution of Schrödinger equation on matlab. However, when I apply boundary conditions, MATLAB only gives me the solution with both coefficients 0. I want to find the solution : Asin(n*pi*x/L) You can see my code below. Could you please tell me where is my mistake...

Hello, I have a little problem understanding the quantum mechanics of a hydrogen atom. Im troubled with the following question: before i measure the state of a (simplified: without fine-, hyperfinestructure) hydrogen atom, which is the right probability density of finding the electron? is it...

Suppose that the spacetime is discrete, with only certain positions being possible for any particle. In this case, the probability distributions of particles have nonzero values at the points on which the wavefunction is defined. Do we need randomness in the transitions of particles in such a...

I apologize for the bad formatting: To start off, I'm trying to use the Schrodinger Equation in the form: (ħ/2m) d^2Ψ(x,t)/dx^2+V(x,t)Ψ(x,t)=EΨ(x,t) I couldn't remember if I need to also take the partial derivative with respect to T as well, but I started off with just X. I plugged in my...

Has anyone formulated a general solution to the time-independent Schrödinger equation in terms of the potential function V(r), and if so, what is it? For any type of V(r). So, instead of a differential equation, a direct relationship between the wavefunction and the potential.

This paper was recently published in the Monthly Notices of the Royal Astronomical Society. Batygin 2018, Schrödinger Evolution of Self-Gravitating Disks I am posting this in here, but I am actually more interested in the implications of looking at this the other way around: namely, from a...

Homework Statement Homework Equations The Attempt at a Solution I understand the equation, and I understand the concept. My question is this: What is the best way to go about solving this problem? My line of reasoning concludes that the fourth lowest energy level is E211. However, the...

I've been studying the 1D schrodinger equation, and getting a feel for solutions in the harmonic oscillator, or potentials of inverse radius (atomic/hydrogen), and many versions of stair-step/ square potentials (square wells.) But, I've noticed that there are very few exact 1D potentials in the...

Hello everyone, For weeks I have been struggling with this quantum mechanics homework involving writing a code to determine the energy spectrum and eigenvalues for the stationary Schrodinger equation for the harmonic oscillator. I can't find any resources anywhere. If anyone could help me get...

Hi everybody, For solving the time dependent Schrödinger equation ##H|\psi(t) \rangle = i\hbar \frac{\partial}{\partial t}|\psi (t)\rangle##, I read in quantum mechanics books the assumption about the solution ##|\psi(t) \rangle## which is made of a linear combination of a complete set of the...

Homework Statement For a wavefunction ##\psi##, the variance of the Hamiltonian operator ##\hat{H}## is defined as: $$\sigma^2 = \big \langle \psi \mid (\hat{H} - \langle\hat{H}\rangle)^2 \psi \big\rangle$$ I want to prove that if ##\sigma^2 = 0##, then ##\psi## is a solution to the...

Homework Statement A particle of mass m in one dimension has a potential: $$V(x) = \begin{cases} V_0 & x > 0 \\ 0 & x \leq 0 \end{cases} $$ Find ##\psi(x)## for energies ##0 < E < V_0##, with parameters $$k^2 = \frac{2mE}{\hbar^2}$$ and $$\kappa^2 = \frac{2m(V_0 - E)}{\hbar^2}$$...

While separating variables in the Schrodinger Equation for hydrogen atom, why are we taking separation constant to be l(l+1) instead of just l^2 or -l^2, is it just to make the angular equation in the form of Associated Legendre Equation or is there a deeper meaning to it?

Homework Statement I want to prove that ##\frac{\partial \langle x \rangle}{\partial t} = \frac{\langle p_x \rangle}{m}##. Homework Equations $$i\hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial^2 \Psi}{\partial x^2} + V \Psi$$ The Attempt at a Solution [/B] So...

Homework Statement Okay, so the question I'm trying to solve is to find the quantized energies for a particle in the potential: $$V(x)=V_0 \left ( \frac{b}{x}-\frac{x}{b} \right )^2$$ for some constant b. The Attempt at a Solution I am following along with the derivation of the quantized...

I have found this one that looks perfect: https://www.amazon.com/dp/331999929X/?tag=pfamazon01-20 THe problem is that it has not been published yet :( , but I can't believe there is no other book on the subject. What I want is to solve numerically the Schrodinger equation with no special...

The analytical solutions are: \begin{equation} \psi(x) = \begin{cases} Ce^{\alpha x}, \text{if } x < -\frac{L}{2}\\ Asin(kx) + Bcos(kx), \text{if } -\frac{L}{2} \leq x \leq \frac{L}{2}\\ Fe^{-\alpha x} , \text{if } x > \frac{L}{2} \end{cases} \end{equation}...

Let's suppose I have a finite potential well: $$ V(x)= \begin{cases} \infty,\quad x<0\\ 0,\quad 0<x<a\\ V_o,\quad x>a. \end{cases} $$ I solved the time-independent Schrodinger equation for each region and after applying the continuity conditions of ##\Psi## and its derivative I ended up with...

Is there a difference between Schrodinger's equation and the wave function? In the beginning of the second edition by David J. Griffiths he compares the classical F(x,t) and Schrodinger's equation and I am having trouble understanding the connection.

Homework Statement [/B] The Hamiltonian and wavefunction for the ground state of the hydrogen atom H(1s1) are given, in atomic units, as ## \hat {H} = - \frac{1}{2} \nabla^2 - \frac {1}{r} ## and ## \phi(1s) = \sqrt {\frac {1}{\pi }} e^{-r} ## . Using the radial portion of the Laplacian in the...

Homework Statement I have the wave function Ae^(ikx)*cos(pix/L) defined at -L/2 <= x <= L/2. and 0 for all other x. The question is: A proton is in a time-independent one-dimensional potential well.What is the probability that the proton is located between x = − L/4 and x = L/4 ? Homework...

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/