Oscillatore Armonico Flashcards
What is the importance of the harmonic oscillator?
It is important in describing the motion of particles near an equilibrium position, such as atoms in a crystal lattice or in a molecule, and is the basis of vibrational spectroscopy. It is also essential in describing the electromagnetic field in a cavity.
What is the potential energy of the harmonic oscillator?
It can be developed around the equilibrium position and expressed as V(x) = 1/2kx^2, where k is the force constant and x is the displacement from equilibrium.
What is the force exerted by the spring on the particle in the harmonic oscillator?
It is an elastic force of the form f = -kx, where k is the force constant and x is the displacement from equilibrium.
What’s the total energy in the harmonic oscillator?
it is the sum of the kinetic and potential energies, given by H = 1/2kA^2 = 1/2mω^2A^2, where A is the amplitude of the oscillation.
What is the probability distribution of finding the particle in the classical harmonic oscillator?
From a classical perspective, the probability of finding the particle is highest at the maximum elongation, when the velocity is reduced to zero before reversing direction.
What is the first step in quantum treatment?
Transforming the classical Hamiltonian into the quantum operator.
What is the quantum operator for the classical Hamiltonian H = p^2/2m + kx^2/2?
H = -h^2/2m * d^2/dx^2 + kx^2/2.
What is the simplified form of the Schrödinger equation after defining α and β?
d^2/dz^2 u(z) + (α/β - z^2) u(z) = 0.
What is the formula for the reduced mass of a diatomic molecule?
μ = m1 * m2 / (m1 + m2).
What is the formula for the energy eigenvalues of the quantum harmonic oscillator?
En = (n + 1/2) * h * ω.
What is the energy of the ground state of the quantum harmonic oscillator?
E0 = h * ω/2.
Qual è la formula delle auto funzioni per l’oscillatore armonico quantico?
ψn(z) = Nne−z2/2Hn(z)
What is the difference between the classical and quantum behavior of the harmonic oscillator?
In the classical behavior, the maximum probability of finding the particle is at the end of the path, while in the quantum behavior, the maximum probability is at the center.
What is an anharmonic oscillator?
An anharmonic oscillator is an oscillator whose potential energy curve is not a parabolic curve and the energy levels are not equidistant.
