Презентация - Introduction to Quantum Mechanic

Introduction to Quantum Mechanic A) Radiation B) Light is made of particles. The need for a quantification 1) Black-body radiation (1860-1901) 2) Atomic Spectroscopy (1888-) 3) Photoelectric Effect (1887-1905) C) Wave–particle duality 1) Compton Effect (1923). 2) Electron Diffraction Davisson and Germer (1925). 3) Young's Double Slit Experiment D) Louis de Broglie relation for a photon from relativity E) A new mathematical tool: Wavefunctions and operators F) Measurable physical quantities and associated operators - Correspondence principle G) The Schrödinger Equation (1926) H) The Uncertainty principle

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Radiations, terminology

Phase speed or velocity

Introducing new variables At the moment, let consider this just a formal change, introducing and we obtain

Introducing new variables At the moment, h is a simple constant Later on, h will have a dimension and the p and E will be physical quantities Then

2 different velocities, v and v

If h is the Planck constant J. s Then

Quantum numbers

Compton effect 1923 playing billiards assuming =h/p

Davisson and Germer 1925

Thomas Young 1773 – 1829

Young's Double Slit Experiment

Young's Double Slit Experiment

Young's Double Slit Experiment

Young's Double Slit Experiment

Linearity The operators are linear: O (a1+ b1) = O (a1 ) + O( b1)

Normalization An eigenfunction remains an eigenfunction when multiplied by a constant O()= o() thus it is always possible to normalize a finite function

Mean value If 1 and 2 are associated with the same eigenvalue o: O(a1 +b2)=o(a1 +b2) If not O(a1 +b2)=o1(a1 )+o2(b2) we define ō = (a2o1+b2o2)/(a2+b2)

Sum, product and commutation of operators (A+B)=A+B(AB)=AB

Sum, product and commutation of operators

Compatibility, incompatibility of operators

x and d/dx do not commute, are incompatible

Introducing new variables Now it is time to give a physical meaning. p is the momentum, E is the Energy H=6. 62 10-34 J. s

Plane waves This represents a (monochromatic) beam, a continuous flow of particles with the same velocity (monokinetic). k, , , p and E are perfectly defined R (position) and t (time) are not defined. *=A2=constant everywhere; there is no localization. If E=constant, this is a stationary state, independent of t which is not defined.

Operators p and H We use the expression of the plane wave which allows defining exactly p and E.

Momentum and Energy Operators

Stationary state E=constant

Kinetic energy

Correspondence principle angular momentum