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LarryS
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What does the Ground State of a quantum simple harmonic oscillator represent physically?
Thanks in advance.
Thanks in advance.
referframe said:What does the Ground State of a quantum simple harmonic oscillator represent physically?
Thanks in advance.
ZapperZ said:This is a rather vague question. For example, is there a reason why you're asking ONLY for the ground state of a SHO? Does this mean that you have no issues with the physical meaning of, say, the ground state of a hydrogenic atom, or a square-well potential? If this is true, then it would be informative to know what you mean in those cases as "represent physically", so that we know what you're looking for.
Zz.
referframe said:From what I have read, the Ground State of a quantum SHO is a gaussian and that state, as an oscillator, has "null vibrations". It is referred to as the "zero-point" energy level and is fundamentally the same as the energy associated with empty space. The ground state of an SHO, because it is a gaussian, minimizes the position-momentum uncertainty.
That is what I have read. I guess I'm trying to visualize what "null vibrations" means.
ZapperZ said:This is getting to be even more puzzling. Gaussian? "null vibrations"?
The SHO wave functions are described via the Hermite polynomials!
Wave functions both in coordinate space and in momentum space are Gaussian as you are well aware. Isn't it enough? I am not sure QM allows further visualization.referframe said:I guess I'm trying to visualize what "null vibrations" means.
vanesch said:... times a gaussian. That's maybe where the poster's expression came from. As H0 is a constant, the wavefunction is a gaussian for the ground state of the SHO.
Wikipedia said:The term "zero-point energy" is a calque of the German Nullpunktenergie. All quantum mechanical systems have a zero-point energy. The term arises commonly in reference to the ground state of the quantum harmonic oscillator and its null oscillations.
The ground state of a SHO is the lowest energy state that the system can occupy. It is the state in which the oscillator is at its equilibrium position and has the lowest possible energy.
The ground state energy of a SHO can be calculated using the formula E0 = 1/2 * hbar * ω, where hbar is the reduced Planck's constant and ω is the angular frequency of the oscillator.
The ground state is significant because it is the starting point for understanding the energy levels and transitions of a SHO. It also represents the lowest energy that the oscillator can have, and all other energy levels are multiples of the ground state energy.
No, the ground state energy of a SHO can never be zero. This is because according to the Heisenberg uncertainty principle, the position and momentum of an oscillator cannot both be known with absolute certainty. As a result, there will always be some minimum energy associated with the ground state.
The ground state of a SHO differs from other energy states in that it has the lowest energy and is the most stable state. Other energy states have higher energies and correspond to the oscillating motion of the oscillator, with the highest energy state being the most unstable. Additionally, the ground state has a quantum number of n=0, while other energy states have higher quantum numbers.