Question

A quantum mechanical simple harmonic oscillator has a 1st excited state with energy 3.3 eV and there are eight spin 1⁄2 particles in the oscillator. How much energy is needed to add a ninth electron. Explain and show your work.

Answer #1

A quantum mechanical simple harmonic oscillator has a 1st
excited state with energy 3.3 eV and there are eight spin-1/2
particles in the oscillator. How much energy is needed to add a
ninth electron. Explain and show your work

A quantum mechanical simple harmonic oscillator has a 1st
excited state with energy 3.3 eV and there are eight spin-1/2
particles in the oscillator. How much energy is needed to add a
ninth electron. Explain and show your work

Quantum mechanics:
Consider a particle initially in the ground state of the
one-dimensional simple harmonic oscillator. A uniform electric
field is abruptly turned on for a time t and then abruptly turned
off again. What is the probability of transition to the first
excited state?

To generate the excited states for the quantum
harmonic oscillator, one repeatedly applies
the raising operator ˆa+ to the ground state, increasing the energy
by ~ω with each step:
ψn = An(ˆa+)
nψ0(x) with En = (n +
1
2
)~ω
where An is the normalization constant and
aˆ± ≡
1
√
2~mω
(∓ipˆ+ mωxˆ).
Given that the normalized ground state wave function is
ψ0(x) = mω
π~
1/4
e
− mω
2~
x
2
,
show that the first...

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+/- 1/2.
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