I The definition of the spectra in quantum mechanics

Asmaa
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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?
 
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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.
 
Asmaa said:
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 Schrodinger 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
 
Can you be more specific about what is unclear? Which of these terms do you not understand?

spectrum

eigenvalues

Schrödinger equation
 
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"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".
 
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...
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