Quantum mechanics unit 1
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Transcript of Quantum mechanics unit 1
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321 Quantum Mechanics Unit 1
Quantum mechanics unit 1• Foundations of QM• Photoelectric effect, Compton effect, Matter waves
• The uncertainty principle
• The Schrödinger eqn. in 1D
• Square well potentials and 1D tunnelling
• The harmonic oscillator
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321 Quantum Mechanics Unit 1
Last time• Photons• Photoelectric effect• Compton effect
• Matter waves• de Broglie relations• Electron diffraction• Waves related to probability
www.le.ac.uk/physics -> people -> Mervyn Roy
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321 Quantum Mechanics Unit 1
Heisenberg uncertainty principle• Fundamental property of quantum systems• Course 3210 Unit 3, Rae Chapter 4
• Inherent uncertainties in predictions – or average spread of a set of repeated measurements
∆ 𝑥 ∆𝑝𝑥≥12ℏ
∆𝐸 ∆ 𝑡≥ 12 ℏ
Heisenberg - formulation of QM 1927, Nobel prize 1932
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321 Quantum Mechanics Unit 1
Example• The position of a proton is known to within 10-11 m.
Calculate the subsequent uncertainty in its position 1 second later.
km
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321 Quantum Mechanics Unit 1
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321 Quantum Mechanics Unit 1
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321 Quantum Mechanics Unit 1
Example• An atom in an excited state emits a photon of
characteristic frequency, n. The average time between excitation and emission is 10-8 s. Calculate the irreducible linewidth of the transition.
Hz
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321 Quantum Mechanics Unit 1
Schrödinger equation
• Developed by induction
• Tested against experiment for over 80 years
• is the wavefunction. This is essentially complex – cannot be identified with any one physical property of the system
Schrödinger - formulation of QM 1925-26, Nobel prize 1933
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321 Quantum Mechanics Unit 1
Schrödinger equation • related to probability
dx
• Wavefunction must be normalised
= 1
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321 Quantum Mechanics Unit 1
Time independent Schrödinger equation
eigenfunction
eigenvalue
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321 Quantum Mechanics Unit 1
Constraints• The wavefunction and its first derivative must be:
• Single valued
• Finite
• Continuous