# Linked Questions

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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
2answers
10k views

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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