The definition of the spectra in quantum mechanics

[Asmaa]

TL;DR

I have read that "The spectrum of a substance (gas, liquid or solid) can be defined as the set of all eigenvalues of the Schrodinger equation"

please, Can anyone explain this?

for undergraduate students how to explain this?

 

[vanhees71]

The sentence is not entirely correct.

You can calculate the spectrum by first solving for the energy eigenvalue problem for the system. Then the spectral lines, i.e., the electromagnetic radiation emitted when the system undergoes transitions from states of higher energy to lower. In first-order perturbation theory what you get are the dipole transitions, and the frequencies of the radiation are given by the energy-differences: $\hbar \omega_{\gamma}=E_n-E_m$, where $E_j$ are the bound-state energies of the system.

 

[PeroK]

Summary:: I have read that "The spectrum of a substance (gas, liquid or solid) can be defined as the set of all eigenvalues of the Schrödinger equation"

please, Can anyone explain this?

for undergraduate students how to explain this?

That's like asking: explain QM to me. You need a textbook. E.g.

https://www.cambridge.org/gb/academ...nics-3rd-edition?format=HB&isbn=9781107189638

 

[jtbell]

Can you be more specific about what is unclear? Which of these terms do you not understand?

spectrum

eigenvalues

Schrödinger equation

 

[laserdan]

Also,

"Spectrum" is quite vague. What kind of spectra? Atomic emission, absorption, fluorescence, inelastic scattering? There are many things to consider in some of these techniques, such as the probability of several relaxation processes, intermolecular and intramolecular interactions, solvents.

Spectroscopy is a messy thing. If we could simply use DFT and other computational techniques to define everything, then spectroscopists would be out of a job, and monkeys could do the work.

You can get close to predicting what might happen when light interacts with matter, but there is no theory that can define a "spectrum".