Linked Questions
14 questions linked to/from What exactly is a bound state and why does it have negative energy?
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Why does negative energy imply that a system is bounded? [duplicate]
I wanted to know why "negative energy" of a two particle system implies
that it is bounded. That is what happens in the case of a hydrogen atom; my textbooks say so, but they do not give any reason ...
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Bound states and negative energy [duplicate]
I have read online that the hydrogen atom's energy level is given by $$E=-13.6eV$$
where $eV$ represents electron volts. The notes say that the energy is negative because the electron is bound to the ...
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What is the mathematical definition of bound state? [duplicate]
While searching why poles of Green’s function corresponds to bound states I came across that I don't know what bound state is. Intuitivaly I know that bound
State should be a state that the ...
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Why can we treat quantum scattering problems as time-independent?
From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this:
Solve the time-independent Schrodinger ...
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Are all bound states normalizeable?
Following Griffiths eq. (2.91) on p. 52 one may define a bound state to be an energy eigenstate
$$H|E\rangle=E|E\rangle\tag{1}$$
with an energy being smaller than the potential far away from the ...
user224659
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Why energy restrictions in the infinite square well are general?
I'm looking at the infinite square well case for solving the Schrodinger equation in quantum mechanics.
I see that when solving the time-independent Schrodinger equation, we find that the energies:
$$...
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What are the exact relations between bound states, discrete spectra, and negative energies in quantum mechanics?
Consider the nonrelativistic quantum mechanics of one particle in one dimension ("NRQMOPOD") with the time-independent Schrodinger equation
$$
\left( -\frac{\hbar^2}{2m} \frac{d^2}{dx^2} + V(...
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Quantum mechanics: bounded states and scattering states
So in quantum physics, we can solve solutions of the schroedinger equation and have that the eigenvalues are either positive or negative, which means it is either a scattering state or a bound state.
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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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The spectrum of the Hamiltonian in quantum mechanics
Consider the Hilbert space $\mathscr{H} = L^{2}(\mathbb{R}^{d})$ and a Hamiltonian:
$$H = -\frac{\hbar^{2}}{2m}\Delta + V(x)$$
for some potential function $V$. States of well-defined energy $E$ are ...
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What is a singular continuous spectrum?
I read some answers about this and the wikipedia page that basically always say that a spectrum can be decomposed into:
$$\mu = \mu_{ac} + \mu_{sc} + \mu_{pp}, $$
where $\mu_{ac}$ is absolutely ...
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Orthogonality of quasibound states
Suppose you have a simple 1D problem with a potential which is such to allow for bound, quasibound, and free states. Are the quasibound states orthogonal to the bound states, or is there some slight ...
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Solution of $p$-wave time independent Schrödinger equation with a simple negative potential
I'm currently self-studying quantum mechanics and have encountered a challenge regarding higher angular momentum wave functions $\phi(r)$ on whether the corresponding Schrödinger equation has a bound ...
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What is the definition of bound state in quantum field theory?
I asked a question a while a go what is a bound state and the question was closed because there is a similar question.
Now since best description we have to describe nature in quantum field theory
How ...
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