Презентация - Introduction to Quantum Mechanic

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Презентация Introduction to Quantum Mechanic


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Introduction to Quantum Mechanic A) Radiation B) Light is made of particles. The need for a quantifi
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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When you find this image, you may skip this part When you find this image, you may skip this part Th
When you find this image, you may skip this part When you find this image, you may skip this part This is less important
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Introduction to Quantum Mechanic, слайд 3
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Radiations, terminology
Radiations, terminology
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Introduction to Quantum Mechanic, слайд 5
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Phase speed or velocity
Phase speed or velocity
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Introducing new variables At the moment, let consider this just a formal change, introducing and we
Introducing new variables At the moment, let consider this just a formal change, introducing and we obtain
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Introducing new variables At the moment, h is a simple constant Later on, h will have a dimension an
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
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2 different velocities, v and v
2 different velocities, v and v
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If h is the Planck constant J. s Then
If h is the Planck constant J. s Then
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Introduction to Quantum Mechanic, слайд 11
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Introduction to Quantum Mechanic, слайд 12
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Introduction to Quantum Mechanic, слайд 13
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Introduction to Quantum Mechanic, слайд 14
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Introduction to Quantum Mechanic, слайд 15
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Quantum numbers
Quantum numbers
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Introduction to Quantum Mechanic, слайд 17
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Introduction to Quantum Mechanic, слайд 18
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Introduction to Quantum Mechanic, слайд 19
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Introduction to Quantum Mechanic, слайд 20
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Introduction to Quantum Mechanic, слайд 21
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Introduction to Quantum Mechanic, слайд 22
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Introduction to Quantum Mechanic, слайд 23
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Compton effect 1923 playing billiards assuming =h/p
Compton effect 1923 playing billiards assuming =h/p
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Davisson and Germer 1925
Davisson and Germer 1925
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Introduction to Quantum Mechanic, слайд 26
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Thomas Young 1773 – 1829
Thomas Young 1773 – 1829
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Young's Double Slit Experiment
Young's Double Slit Experiment
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Young's Double Slit Experiment
Young's Double Slit Experiment
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Young's Double Slit Experiment
Young's Double Slit Experiment
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Young's Double Slit Experiment
Young's Double Slit Experiment
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Introduction to Quantum Mechanic, слайд 32
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Introduction to Quantum Mechanic, слайд 33
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Introduction to Quantum Mechanic, слайд 34
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Introduction to Quantum Mechanic, слайд 35
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Introduction to Quantum Mechanic, слайд 36
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Introduction to Quantum Mechanic, слайд 37
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Introduction to Quantum Mechanic, слайд 38
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Introduction to Quantum Mechanic, слайд 39
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Introduction to Quantum Mechanic, слайд 40
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Introduction to Quantum Mechanic, слайд 41
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Introduction to Quantum Mechanic, слайд 42
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Linearity The operators are linear: O (a1+ b1) = O (a1 ) + O( b1)
Linearity The operators are linear: O (a1+ b1) = O (a1 ) + O( b1)
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Normalization An eigenfunction remains an eigenfunction when multiplied by a constant O()= o() t
Normalization An eigenfunction remains an eigenfunction when multiplied by a constant O()= o() thus it is always possible to normalize a finite function
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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(
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)
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Sum, product and commutation of operators (A+B)=A+B(AB)=AB
Sum, product and commutation of operators (A+B)=A+B(AB)=AB
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Sum, product and commutation of operators
Sum, product and commutation of operators
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Compatibility, incompatibility of operators
Compatibility, incompatibility of operators
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x and d/dx do not commute, are incompatible
x and d/dx do not commute, are incompatible
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Introducing new variables Now it is time to give a physical meaning. p is the momentum, E is the Ene
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
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Plane waves This represents a (monochromatic) beam, a continuous flow of particles with the same vel
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.
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Introduction to Quantum Mechanic, слайд 52
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Operators p and H We use the expression of the plane wave which allows defining exactly p and E.
Operators p and H We use the expression of the plane wave which allows defining exactly p and E.
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Momentum and Energy Operators
Momentum and Energy Operators
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Stationary state E=constant
Stationary state E=constant
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Kinetic energy
Kinetic energy
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Correspondence principle angular momentum
Correspondence principle angular momentum
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Introduction to Quantum Mechanic, слайд 58
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Introduction to Quantum Mechanic, слайд 59
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Introduction to Quantum Mechanic, слайд 60
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Introduction to Quantum Mechanic, слайд 61
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Introduction to Quantum Mechanic, слайд 62
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Introduction to Quantum Mechanic, слайд 63
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Introduction to Quantum Mechanic, слайд 64
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Introduction to Quantum Mechanic, слайд 65
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Introduction to Quantum Mechanic, слайд 66
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Introduction to Quantum Mechanic, слайд 67
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Introduction to Quantum Mechanic, слайд 68
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Introduction to Quantum Mechanic, слайд 69
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Introduction to Quantum Mechanic, слайд 70


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