Linked Questions

7
votes
1answer
285 views

Can I determine the potential term in the Schrödinger equation based on the eigenvalues? [duplicate]

Let's imagine I knew a certain system could be described by a one-dimensional Schroedinger equation. I know the mass/momentum term, but not the shape of the potential. Further for some reason I know ...
5
votes
1answer
130 views

Can we reconstruct 1D potentials in QM from the spectrum? [duplicate]

Knowing the potential, we can find the spectrum of the Schrödinger operator. The converse question is: Knowing the spectrum, can we reconstruct the potential? As an example, a harmonic potential has ...
0
votes
1answer
184 views

Arriving at the Quantum Mechanial Potential From The Energy Eigenvalues [duplicate]

In Quantum Mechanics, we know that given a potential we can solve the eigen value problem to find out the energy eigen values and eigen functions. Now suppose in an experiment we have information only ...
0
votes
0answers
44 views

Is the there a unique correspondence between the potential and bound state wave functions? [duplicate]

I'm asking specifically for the schrodinger equation. Is there a unique correspondence between the energy eigenfunctions $\phi_i(x)$ and the potential term $U(x) = V(x)\phi(x)$? Furthermore, is this ...
1
vote
1answer
41 views

Deriving system properties from energy spectrum [duplicate]

To what extent can we derive the properties of a system given the existence of a hermitian operator with a particular spectrum? For example, if we know that there exists a hermitian operator with ...
0
votes
0answers
40 views

One-dimensional Schrödinger equation: reproducing a given set of energy values [duplicate]

Given a set of $N$ increasing real numbers $\{E_1, E_n, \cdots, E_N \}$, is it always possible to find a potential $V(x)$ such that the set of $\{E_j\}$ are the lowest eigenvalues of the corresponding ...
19
votes
4answers
2k views

Is it possible to reconstruct the Hamiltonian from knowledge of its ground state wave function?

Is it possible to "construct" the Hamiltonian of a system if its ground state wave function (or functional) is known? I understand one should not expect this to be generically true since the ...
17
votes
6answers
2k views

Is the harmonic oscillator potential unique in having equally spaced discrete energy levels?

I was wondering if the good old quadratic potential was the only potential with equally spaced eigenvalues. Obviously you can construct others, such as a potential that is infinite in some places and ...
5
votes
2answers
10k views

Eigenstates of half Harmonic Oscillator [closed]

This might be a stupid question so pardon me! If I am looking for energy eigenstates to the 1D quantum problem such that there is an infinite barrier at $x<0$ and for $x>0$ the potential is $kx^...
8
votes
2answers
1k views

_Actually_ hearing the shape of a drum

The problem of hearing the shape of a drum is well known as a mathematical problem. But what about as a problem of (1) physics and (2) human perception? Suppose you have the kind of membrane used ...
2
votes
1answer
2k views

Calculating Ground State Energy in 1D Potential

Given potential $V(x) = Asec(x)$ for $x > 0$. I want to calculate the ground-state energy $E_0$ via the Schrödinger equation. I'm completely stuck on this one. I've set up the time-independent ...
5
votes
2answers
180 views

Do asymptotically similar potentials yield similar energy levels asymptotically?

Let there be given two Hamiltonians $$H_1~=~ p^{2}+f(x) \qquad \mathrm{and} \qquad H_2~=~ p^{2}+g(x). $$ Let's suppose that for big big $x$, the potentials are asymptotically similar in the sense ...
2
votes
3answers
133 views

Is it possible to reconstruct the wavefunction of a molecule from a collection of spectra?

Spectra of a molecule can be calculated if the wavefunction is known. Is it possible to do the opposite?
1
vote
1answer
384 views

Is it possible to calculate a potential given period of oscillation as a function of energy?

Suppose I have a smooth potential $U:\mathbb R\to\mathbb R$ with $U(x)=U(-x)$, $U(0)=0$, and $U'(x)>0$ for $x>0$. A particle of mass $1$ at rest at position $x=x_0$ has total energy $U(x_0)$, ...
3
votes
0answers
450 views

Determine the number of bound states admitted in Schrodinger system

Is there a general method for determining the number of bound states admitted by a potential in the Schrodinger equation? Certainly the number of dimensions must factor in somehow: the delta ...

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