phy-4600/book_notes/chap3/Bohr Frequency
2016-02-12 12:26:39 -05:00

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Ψ(t) is the time-revolving state function,
Ψ(t) = c₁ exp(-ι E₁/ħ t) + c₂ exp(-ι E₂/ħ t) + ...
The eigenstate of A corresponding to the eigenvalue a₁
|a₁〉 = α₁|E₁〉 + α₂|E₂〉
The probability of measuring the eigenvalue a₁ is
P(a₁) = |〈a₁|Ψ(t)〉|²
↓ Derivation on page 71
P(a₁) = |α₁|²|c₁|² + |α₂|²|c₂|² + Re(α₁c₁⃰α₂⃰c₂ exp(-ι (E₂-E₁)/ħ t))
The Bohy Frequency (angular frequency) of two states E₁ and E₂ is thus revealed:
ω₂₁ = (E₂ - E₁)/ħ