# Презентация - Introduction to Quantum Mechanic

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Pic.1 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
Pic.2 When you find this image, you may skip this part When you find this image, you may skip this part This is less important
Pic.3 Pic.4 Pic.5 Pic.6 Phase speed or velocity
Pic.7 Introducing new variables At the moment, let consider this just a formal change, introducing and we obtain
Pic.8 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
Pic.9 2 different velocities, v and v
Pic.10 If h is the Planck constant J. s Then
Pic.11 Pic.12 Pic.13 Pic.14 Pic.15 Pic.16 Quantum numbers
Pic.17 Pic.18 Pic.19 Pic.20 Pic.21 Pic.22 Pic.23 Pic.24 Compton effect 1923 playing billiards assuming =h/p
Pic.25 Davisson and Germer 1925
Pic.26 Pic.27 Thomas Young 1773 – 1829
Pic.28 Young's Double Slit Experiment
Pic.29 Young's Double Slit Experiment
Pic.30 Young's Double Slit Experiment
Pic.31 Young's Double Slit Experiment
Pic.32 Pic.33 Pic.34 Pic.35 Pic.36 Pic.37 Pic.38 Pic.39 Pic.40 Pic.41 Pic.42 Pic.43 Linearity The operators are linear: O (a1+ b1) = O (a1 ) + O( b1)
Pic.44 Normalization An eigenfunction remains an eigenfunction when multiplied by a constant O()= o() thus it is always possible to normalize a finite function
Pic.45 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)
Pic.46 Sum, product and commutation of operators (A+B)=A+B(AB)=AB
Pic.47 Sum, product and commutation of operators
Pic.48 Compatibility, incompatibility of operators
Pic.49 x and d/dx do not commute, are incompatible
Pic.50 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
Pic.51 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.
Pic.52 Pic.53 Operators p and H We use the expression of the plane wave which allows defining exactly p and E.
Pic.54 Momentum and Energy Operators
Pic.55 Stationary state E=constant
Pic.56 Kinetic energy
Pic.57 Correspondence principle angular momentum
Pic.58 Pic.59 Pic.60 Pic.61 Pic.62 Pic.63 Pic.64 Pic.65 Pic.66 Pic.67 Pic.68 Pic.69 Pic.70 Если вам понравился сайт и размещенные на нем материалы, пожалуйста, не забывайте поделиться этой страничкой в социальных сетях и с друзьями! Спасибо!                    