Quantum Mechanics Flashcards
What are the three failures of classical physics?
Black-body radiation.
Heat capacity at low temperatures.
Spectroscopy.
How does black body radiation fail in classical physics?
It agrees at high wavelengths, but fails at lower wavelengths. This was solved by introducing discrete energies.
How does heat capacity at low temperatures fail in classical physics?
Classical physics predicts heat capacity doesn’t change with temperature but it does at very low temperatures. This was solved by introducing the quantisation of energy.
How does spectroscopy fail in classical physics?
Spectroscopy shows discrete values.
What is the correspondence principle?
Quantum mechanics reproduces classical physics in the limit of large quantum numbers.
What is wave-particle duality?
The concept that every particle can show the properties of particles and waves.
How can the probability of finding the particle be calculated?
Integrating the square of the wavefunction over the limits of the area.
How do you know when a wavefunction is normalized?
Integrating the square of the wavefunction over all space. This should equal 1.
When are two wavefunctions orthogonal?
∫Ψi*Ψjdτ = 0 where i≠j
What is the expectation of an operator?
<Ω> = ∫Ψ*ΩΨdτ / ∫Ψ*Ψdτ
</Ω>
What is the time-independent Schrodinger equation?
HΨ = EΨ
