All Questions
Tagged with potential-energy schroedinger-equation
63
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Quantum Harmonic Oscillator With a Linear "Perturbation"
It is well known that the energy solutions for the unidimensional quantum harmonic oscillator $V(x) = \frac{1}{2}m\omega^2x^2$ are $E_n = (n + \frac{1}{2})\hbar\omega, n \in \mathbb{N}$. In particular,...
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Clarification on bound states: do "locally bound" states exist?
In Griffiths, a state with energy $E$ is said to be "bound" if $$E < \min\left(\lim_{x\to\infty} V(x), \lim_{x\to-\infty} V(x)\right)$$ (i.e. $E$ is less than both of those quantities). ...
- 149
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Unbound States of the 1D Finite Potential Well [closed]
Edit: After writing a Python code to numerically solve the constraint problem on the coefficients with Gauss-Jordan elimination, it seems that the biggest problem was that I was treating the ...
- 3,202
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Applications of infinite square well/particle in a box
I know of only two instances where the infinite square well is an adequate model for experimental behaviour: the absorption wavelengths of cyanine dyes, and extremely small semiconductors to which ...
- 101
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Schrödinger-Propagator for combined linear and harmonic potential
Given the Hamiltonian
\begin{equation}
H = \frac{p^2}{2m} + V(x)
\end{equation}
The propagator for a pure harmonic potential of the form
\begin{equation}
V(x) = \frac{1}{2} m \omega^2 x^2
\end{...
- 141
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230
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How to derive bound and unbound states for an absolute value potential?
How do you find for what range of energies the absolute value potential has bound and unbound states?
What I have understood from my previous Intro to Quantum lectures are that in order to derive the ...
- 51
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How to prove the bound and scattering states theorem? [duplicate]
In Griffiths it is mentioned that if the energy eigenvalue is less than the value of the potential at + and - infinity, then we have bound states. If however the energy is bigger than the potential at ...
- 369
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Which potentials in real life are separable in variables?
We usually see in 3d potential problems, that we consider potential to be separable as a sum of three independent one dimensional like potential, for all three variables, i.e
$$V(x, y, z)=V(x)+V(y)+V(...
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147
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Vanishing zero point energy in harmonic oscillator
In classical mechanics, adding a constant to the potential changes nothing. In quantum mechanics, this just shifts the energy and multiples the wavefunction with a phase term.
But now suppose I use ...
- 1,931
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433
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Finite potential well and nature of its solutions
The question I have is about nature of solutions, not a solution or a specific answer that I am looking for. If we define a potential well centred at $x=0$ as the following,
$$V(x) = \left\{ \begin{...
- 131
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Understanding the radial equation, why is the left hand side different from the right hand side?
Im studying the hydrogen atom and Ive realized that one side of the radial differential equation isnt equal to the other. What am I getting wrong?
Knowing that the potential for the hydrogen atom is $$...
user348127
3
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2
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996
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Schrödinger Equation Energy Requirement $E \geq V_{\min}$
Problem 2.2 of Griffiths' Intro to Quantum Mechanics states that
"$E$ must exceed the minimum value of $V(x)$ for every normalizable solution to the time-independent Schrödinger equation."
...
- 802
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232
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Step potential bound states not bound
According to Griffiths, if the energy is less than the potential at −∞ and +∞ then the state is bound. For the step potential this would be if the energy is less than the step height. But there are no ...
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Classical analog of the statement "$E$ must exceed the minimum value of $V(x)$
Overall question:
Griffiths problem 2.2 states that $E$ must exceed the minimum value of $V(x)$ for every normalizable solution to the time-independent Schrodinger equation. Then, it asks for a proof ...
- 1,261
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Discrete Spectrum vs Continuous Spectrum and Bounded, Scattering States
Apolgies in advance if this is a confusing ramble and multitude of questions, I'm not quite sure how to articulate myself. I am currently reading up on quantum mechanics and seem to have confused ...
