All Questions
17
questions
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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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1
answer
120
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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 ...
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1
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226
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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
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2
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810
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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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1
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383
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Reasoning of no negative energy states in the quantum harmonic oscillator [duplicate]
In Griffiths' text on QM, I am trying to understand his logic as to why there can be no states of negative energy. He writes:
What if I apply the lowering operator repeatedly? Eventually I'm going to ...
- 753
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0
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31
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Minimum energy eigenvalue [duplicate]
Why is the energy eigenvalue is always greater than minimum potential for a particle moving in a certain potential?
1
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1
answer
156
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Odd function (probability density function) describing the measurable quantity of a quantum particle [closed]
This question is in reference to Quantum Physics of Atoms, Molecue, Solids, Nuclei and particles by Robert Eisberg and Robery Resnick.
The setup for an infinite square quantum well with the potential ...
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1
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665
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How can Bound state energy be negative if the $V_{min}$ is positive? [duplicate]
We know that Energy must be negative for bound states (as the wavefunction must go to 0 at infinity) but when we are looking at potential wells, we also say that E must be greater than the minimum ...
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1
answer
129
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Why must normalisable eigenfunctions have $E > V_{min}$? [duplicate]
I have read normalisable eigenfunctions of the Hamiltonian operator.
$$\hat{H}\phi = E\phi$$
If $\phi$ is to be normalisable we must have $E > V_{min}$
Why is this?
- 267
2
votes
2
answers
1k
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Why can't energy be below the minimum of the potential in a bound state? [duplicate]
I just stumbled across the problem and have no idea how to solve it:
"Considering the Time-Independent Schrodinger Equation for a stationary state $\psi$ with energy $E$, that is $$\psi '' = \...
- 418
1
vote
2
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356
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Is this the reason for vanishing of wavefunction beyond the infinite walls?
Merzbacher in his Quantum Mechanics says that for the "particle in a box" potential ($V(x) = 0$ for $|x|\le L$ and $+\infty$ otherwise),
Since the expectation value of the potential energy ...
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3
votes
3
answers
3k
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Why Energy is greater than min value of Potential in Bound state?
Griffiths describes bound and scattering states as follows:
Bound state : $E<V(-\infty $) and $V(+\infty $)
Scattering state: $E>V(-\infty)$ or $V(+\infty)$
Why is that Energy for a ...
- 432
34
votes
5
answers
16k
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Heisenberg Uncertainty Principle Applied to an infinite square well
I appreciate the statement of Heisenberg's Uncertainty Principle. However, I am a bit confused as to how exactly it applies to the quantum mechanical situation of an infinite square well.
I understand ...
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4
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2
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3k
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When we say particle in a box has quantized energy, is that kinetic or total energy?
In quantum mechanics, it is usually said that energy of the bound (constrained) systems such as particle in a box (infinite potential well) is quantized. It confuses me exactly what type of energy is ...
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2
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210
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Why are the allowed energies a continuum in the region $V_{\_} < E < V_{+}$?
I'm studying quantum mechanics and I don't quite understand why there's an energy continuum in the region $V_{\_} < E < V_{+}$ in the following example:
It was explained that because of the ...
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