KI2141 SIK Lecture01 TeoriKuantum

Quantum Theory

Achmad Rochliadi

Introduction and Principles

For Personal Use Only !!!

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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.




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Black-body radiations

Experimental realization : cavity at temperature T, equilibrium between radiation and wall material; pinhole emits black-body radiation



A hot object emits EM radiation. Perfect absorber = perfect emitter.


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Energy distribution in Black-body Origin of quantum mechanics


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 :



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 :



Planck distribution : For Personal Use Only !!!

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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 :



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.



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 :




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Atomic and molecular spectra

Atom and molecular spectra show quantization of energy.



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).


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


Wave-particle duality

de Broglie relation


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Electron microscope

Resolution limitiation of classic microscope → replace light with electron. SEM, TEM.


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.


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 :


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.



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



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


The solution are


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Information in a wavefunction

Verification of the solutions




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The probability density

Suppose A is set arbitrary and B = 0 then the wave function is.



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.



The existence of the particles is showed by the probability density


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The probability densityQuantum mechanics principles



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Operator, eigenvalue and eigenfunctions

To extract information from the the wavefuntion, Schrodinger equation is rewritten as



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)



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


KI2141 SIK Lecture01 TeoriKuantum

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