# Questions tagged [schroedinger-equation]

Partial differential equation which describes the time evolution of the wavefunction of a quantum system. It is one of the first and most fundamental equations of quantum mechanics.

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### How do I use first-order perturbation theory to compute the first four energy levels related to a potential well?

I came across a problem whose statement is as follows: An electron moves in the potential well $P (x) = -\delta$ for $- a <x <0$ and $P (x) = \delta$ for $0 <x <a$ (Fig. 13.7). Use first-...
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### How to correct eigenvalues for infinite square well potential using numerov matrix method? [closed]

i was using this code infinite was approximated by 10^10. But the energy eigen values that i got is completely different from the actual .How to resolve ...
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### Solving the energy spectrum for a $\cot^2$ potential well using the WKB approximation

I am taking graduate quantum mechanics, and we are now discussing the WKB/semiclassical approximation. I am trying to solve a problem where I would need to find the energy spectrum of the 1D motion in ...
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### Can we handle the wave function as if it was a real valued function? [duplicate]

I am trying to analyze in general simple one dimensional QM problems. To be more specific let's consider this kind of Hamiltonian: $$H=\frac{\hat{p}^2}{2m}+V(\hat{x})$$ From this one we can derive the ...
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### Expectation value in the Schrödinger Equation

The Schrödinger equation is given by: $$i \hbar \partial_t |\Psi\rangle = \hat{H}|\Psi\rangle$$ The right hand side is just an operator acting on a state vector, so we are free to consider its ...
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### How can matter, the things which we can touch and feel on a macro level, exhibit a wave nature?

Louis de Broglie suggested that, if a particle like electron has momentum and wavelength associated with it (due to Planck's constant), then it might be a wave. The region where it exists are those ...
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### What does $V(r)$ mean in the Schrodinger equation?

The Schrodinger equation: $$-\frac{\hbar^2}{2m}\nabla^2\Psi(r)+V(r)\Psi(r)=E\Psi(r)$$ $$\textit{kinetic energy} + \textit{potential energy}=\textit{total energy}$$ Is one of my favourite equations, ...
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### B.C. for time-decaying delta barrier inside an infinite well

So let's say I have an infinite well with walls up at $x=-L$ and $x=L$. Suppose that inside the well, there is a time-dependent potential $$V(x,t)= \alpha_0\delta{(x)}f(t)$$ where $f(t)$ is a ...
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### Do energy levels ever appear at the peak of a cosine potential in higher dimensions?

I simulated a hyperspherically symmetric wavefunction for the case of $V=-\cos(r)$, in which $h=1$, and $m=1$ and the number of spatial dimensions is $4$. I charted the integral of the square of the ...
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### How can we form Euler-Lagrange equations for Time-Independent Schrodinger Equations?

Is it possible to form a lagrangian of the TISE using the concept of Lagrange Multipliers? I am new to this topic so any help would be much appreciated.
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### Finding the wave function at all times for a particle trapped in an infinite potential well, given the initial wave function of the particle [closed]

A particle is trapped in the region $0 \leq x \leq \pi$ by an infinite potential well. At the initial time, the particle has a wavefunction $\psi(x, 0)=A(\sin (x)+\sin (2 x))$. Find the wavefunction ...
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### Determining the motion of a classical particle and quantum particle in a given potential with a given initial position and energy [closed]

How do I go about solving this? I know bound states require the energy to be less than the potential while scattering states require the energy to be greater than the potential. I also know that ...
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### How does a sine wave evolve under the Schrodinger equation?

On pg 72 of "Something Deeply Hidden," Sean Carroll discusses how the uncertainty principle is just a consequence of the Schrodinger equation. He writes: Consider a simple sine wave, ...
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