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EP 228: Quantum Mechanics
- P. Ramadevi, 2nd floor Dept of
References
- Griffiths-Introduction to Quantum
Mechanics
- Sakurai – Modern Quantum
Mechanics
- Shankar-Principles of Quantum
EP 228: Quantum Mechanics P. Ramadevi, 2 nd floor Dept of Physics, - - PowerPoint PPT Presentation
EP 228: Quantum Mechanics P. Ramadevi, 2 nd floor Dept of Physics, - - PowerPoint PPT Presentation
EP 228: Quantum Mechanics P. Ramadevi, 2 nd floor Dept of Physics, IIT Bombay rama0072006@gmail.com Extn: 7563 References Griffiths-Introduction to Quantum Mechanics Sakurai Modern Quantum Mechanics Shankar-Principles of
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In-Sem, End-sem
- Two 10 marks quiz (one in first week
- f Feb and other in the last week of
March)
- Mid-Sem 30 marks
- End-Semester 40 marks
- Assignment 10 marks
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Before Mid-Sem
- Review quantum ideas
(Wavefunction formalism)
- Linear vector spaces
- Operator, state vecor formalism of
Harmonic oscillator
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After Mid-Sem
- Hydrogen atom, Angular Momentum
- Spin
- Addition of angular momentum
- Clebesh-Gordan coefficients
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Limitations of Classical ideas- need for Quantum theory
- Experimental data in the Microscopic World (inside an
atom or nucleus) – classical laws are inadequate
1) Black-Body Spectrum 2) Photo-electric effect 3) Compton scattering
Needed introduction of a fundamental constant h (Planckconstant) leading to the `Quantum’ regime Photons obey E= hν and using relativistic energy for massless particles imply momentum of photon p=h/ λ
Daring proposal of de-Broglie: equation for the wavelength of matter waves must obey the same equation of photon momentum
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Matter waves
- For an electron moving in a circular orbit of
radius r, constructive interference of the electron wave with itself in the orbit requires 2 πR = n λ
- Substituting de-Broglie proposal gives Bohr
quantization mvr= n h/2π
- Electron diffraction expts : Davisson-Germer
(confirms wave nature of electron)
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Interference expt
plot C for electron beam is observed (wave info)
The plot is actually probability curve for electron
Attempting which slit the electron came from gives plot B(particle info)
Either particle or wave nature can be observed
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Wave-particle duality
- Classical Mechanics
- both x, p can be
simultaneously found
- Equation is
Newton’s law determines x,p
- Quantum Mechanics
- x,p cannot be simultaneously
determined precisely-
Heisenberg’s uncertainty principle
- Equation is Schrodinger eqn
which determines probability amplitude Ψ(x,t) (complex) whose modulus squared gives probability
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Particle nature of light
Blackbody radiation Photo-electric Effect Compton effect Wave-nature
- f particles
(de-Broglie wave) Diffraction experiment Uncertainty principle Wavepacket, probability Average Schrodinger Eqn Matter wave
Quantum Mechanics
We will see in detail
Flow chart
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Wave-function
< ∞ (for square
Integrable)
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Square-Integrable functions
- Square integrable wavefunction Ψ(x,t) must
go to zero faster than 1/√|x| as |x| -> +∞
- We can normalize such functions giving
normalised wavefunction obeying
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Normalisation constant
Where N is finite Normalised wavefunction The normalisable wavefunctions satisfy Using time-dependent Schrodinger equation, show that Exercise 1
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More Exercises
2) Starting from expectation value of x, show Exercise 3 Ehrenfest Theorem- expectation values obey classical laws
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Discontinuous potentials V(x)
Step function at x=0
For finite potentials, show that
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