ki2141 sik lecture01 teorikuantum
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Teori KuantumTRANSCRIPT
Quantum Theory
Achmad Rochliadi
Introduction and Principles
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Contents Quantum Theory
1. Origin of quantum mechanic
2. The dynamic of microscopy system
3. Quantum mechanical principles
- The Schrodinger equation- The Bohr interpretation of the wave function
- The failure of classical physics- Wave particle duality- Impact on biology : Electron microscopy
- The information in a wavefunction- The uncertainty principles- The postulate of quantum mechanics
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Classical mechanics (CM)
CM predict a precise trajectory for particles with specific location and momenta.
CM allow translational, rotational and vibrational mode to be excited to any energy by control the force given.
CM does not work on transfering small energies to a small particles.
Origin of quantum mechanics
Failures of classical physics
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Light in classical mechanics
Light in CM is a electromagnetic radiation, ie. An oscilation electric and magnetic disturbance that spread as a harmonic wave.
Origin of quantum mechanics
Failures of classical physics
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Black-body radiations
Experimental realization : cavity at temperature T, equilibrium between radiation and wall material; pinhole emits black-body radiation
Origin of quantum mechanics
Failures of classical physics
A hot object emits EM radiation. Perfect absorber = perfect emitter.
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Energy distribution in Black-body Origin of quantum mechanics
Failures of classical physics
CM explation by Lord Rayleigh : The EM is collection of oscillators of all possible frequencies
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Rayleigh-Jean Law
Equipartition is used to calculate the average energy of each oscillator as kT.
Rayleigh-Jean law :
Origin of quantum mechanics
Failures of classical physics
Only work on low frequencies.
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Planck distribution
Propose that the energy of each electromagnetic oscillator is limited to discrete values and cannot be varied arbitrarily → Quantization of energy.
Permitted energy :
Origin of quantum mechanics
Failures of classical physics
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Heat capacities
The mean energy of an atom as it oscillates about its mean position in a solid is kT for each direction of displacement. In three dimensions, the average energy of each atom is 3kT; for N atoms the total energy is 3NkT.
The molar internal energy :
Origin of quantum mechanics
Failures of classical physics
The molar constant volume heat capacity
Aggreable with Dulong-Petit experiment
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Heat capacities
It was found that the molar heat capacities of all monatomic solids are lower than 3R at low temperatures, and that the values approach zero as T→0.
Origin of quantum mechanics
Failures of classical physics
Einstien assumed that atom oscilated with a single frequency. For Personal Use Only !!!
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Heat capacities
Einstein expression for the molar heat capacity :
Origin of quantum mechanics
Failures of classical physics
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Atomic and molecular spectra
Atom and molecular spectra show quantization of energy.
Origin of quantum mechanics
Failures of classical physics
Emission of exited Fe Absoprtion of SO2 molecules.
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Particle character of EM radiation
Particle of EM are photon and have discreed energy. Particle-like character is showed in photoelectric effect. (Ejection of
electrons from metal when expose to uv radiation).
Origin of quantum mechanics
Wave-particle duality
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Wave character of particles
The Davisson–Germer experiment. The scattering of an electron beam from a nickel crystal shows a variation of intensity characteristic of a diffraction experiment in which waves interfere constructively and destructively in different directions
Origin of quantum mechanics
Wave-particle duality
de Broglie relation
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Electron microscope
Resolution limitiation of classic microscope → replace light with electron. SEM, TEM.
Origin of quantum mechanics
Impact in biology
A TEM image of a cross-section of a plant cell showing chloroplasts, organelles responsible for the reactions of photosynthesi.Chloroplasts are typically 5 µm long
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Schrodinger equation
Quantum mechanics, wave-particles duality of matter travel not along a definite path but the particle is distributed throught space like a wave
Trajectory replaced by a wave function, Ψ (psi) Equation for finding the wavefunction of any system.
Dynamics of microscopic sys.
Schrodinger equation
It a time-dependent Schrodinger equation of mass moving in a one dimention with energy E. 3 dim in pg 255
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Probability Dynamics of microscopic sys.
Born interpretataion
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Bohrn interpretattion of Ψ
The wavefunction contains all the dynamical information about the system it describes
The square of the amplitude of an electromagnetic wave in a region is interpreted as its intensity → the probabilistic of finding particles
The probability density :
Dynamics of microscopic sys.
Born interpretataion
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Normalisation of wavefunction
If Ψ is a solution, so is NΨ. → by the N constant a “proportionality” become an equality.
Dynamics of microscopic sys.
Schrodinger equation
Normalisation is evaluated by
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Quantisation of wavefunction
Principles restriction of Ψ : Ψ must not infinite
anywhere Ψ must single valued First derivative is
continuous Second derivatif of Ψ
must be well-defined and continuous
Dynamics of microscopic sys.
Schrodinger equation
Unacceptable wavefunctions
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Information in a wavefunction
The Schrödinger equation for a particle of mass m free to move parallel to the x-axis with zero potential energy
Quantum mechanics principles
Schrodinger equation
The solution are
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Information in a wavefunction
Verification of the solutions
Quantum mechanics principles
Schrodinger equation
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The probability density
Suppose A is set arbitrary and B = 0 then the wave function is.
Quantum mechanics principles
Schrodinger equation
The existence of the particles is showed by the probability density
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The probability density
Suppose A is set arbitrary and B = 0 then the wave function is.
Quantum mechanics principles
Schrodinger equation
The existence of the particles is showed by the probability density
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The probability densityQuantum mechanics principles
Schrodinger equation
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Operator, eigenvalue and eigenfunctions
To extract information from the the wavefuntion, Schrodinger equation is rewritten as
Quantum mechanics principles
Schrodinger equation
For 1 dimension
Operator something that carries out a mathematical operation on the function ψ
Operator Eigenfunction Eigenvalue For Personal Use Only !!!
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Operator, eigenvalue and eigenfunctions
General form : (Operator)(function) = (constant factor) x (same function)
Quantum mechanics principles
Schrodinger equation
Position and momentum operator : For Personal Use Only !!!
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It is impossible to specify simultaneously, with arbitrary precision, both the momentum and the position of a particle.
The uncertainty principleQuantum mechanic principles
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Wave function. All dynamical information is in the wave function, it can be found by solving Schrodinger equation for the system.
The Born interpretation. If the wave function have a value at some point, then the probability of finding the particles is propotional to
Acceptable wavefunction. It has to be continous, have a continous first derivative, singled value and square-integrable
Observables. Observables, Ω, are reprensented by operator, build from position and momentum operator of the form
The Heisenberg uncertainty principles. It is imposible to specify
simultaneously with arbitary precision, both the momentum and position of a particles.
The postulate of quantum mechanicQuantum mechanic principles
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