Review of Early antum Mechanics Formalization of antum Mechanics Physics 280 antum Mechanics Lecture Spring 2015 Dr. Jones1 1Department of Physics Drexel University August 3, 2016 Dr. Jones Physics 280 antum Mechanics Lecture Schrodinger’s¨ Wave Equation Heisenberg Uncertainty Strange Consquences Strange Contradictions Review of Early antum Mechanics Formalization of antum Mechanics Objectives Review Early antum Mechanics Dr. Jones Physics 280 antum Mechanics Lecture Heisenberg Uncertainty Strange Consquences Strange Contradictions Review of Early antum Mechanics Formalization of antum Mechanics Objectives Review Early antum Mechanics Schrodinger’s¨ Wave Equation Dr. Jones Physics 280 antum Mechanics Lecture Strange Consquences Strange Contradictions Review of Early antum Mechanics Formalization of antum Mechanics Objectives Review Early antum Mechanics Schrodinger’s¨ Wave Equation Heisenberg Uncertainty Dr. Jones Physics 280 antum Mechanics Lecture Strange Contradictions Review of Early antum Mechanics Formalization of antum Mechanics Objectives Review Early antum Mechanics Schrodinger’s¨ Wave Equation Heisenberg Uncertainty Strange Consquences Dr. Jones Physics 280 antum Mechanics Lecture Review of Early antum Mechanics Formalization of antum Mechanics Objectives Review Early antum Mechanics Schrodinger’s¨ Wave Equation Heisenberg Uncertainty Strange Consquences Strange Contradictions Dr. Jones Physics 280 antum Mechanics Lecture Classical Physics predicts that the intensity of radiation from blackbody-like sources goes to infinity with decreasing wavelength, which is experimentally shown to be untrue and is impossible anyway. Planck uses a mathematical trick for the first time ever–energy quantization: E = hf to ”fix” the equations. Einstein takes this result at face value and shows that photons are quantized in the same way, explaining the photoelectric eect. Bohr adapts the idea of quantization to ”explain” the Rydberg equation and why the emission/absorption spectrum is quantized. He quantizes angular momentum. Review of Early antum Mechanics Formalization of antum Mechanics So far.. Electrical charges are quantized in the form of electrons and protons, nothing is smaller than ±e. Dr. Jones Physics 280 antum Mechanics Lecture Planck uses a mathematical trick for the first time ever–energy quantization: E = hf to ”fix” the equations. Einstein takes this result at face value and shows that photons are quantized in the same way, explaining the photoelectric eect. Bohr adapts the idea of quantization to ”explain” the Rydberg equation and why the emission/absorption spectrum is quantized. He quantizes angular momentum. Review of Early antum Mechanics Formalization of antum Mechanics So far.. Electrical charges are quantized in the form of electrons and protons, nothing is smaller than ±e. Classical Physics predicts that the intensity of radiation from blackbody-like sources goes to infinity with decreasing wavelength, which is experimentally shown to be untrue and is impossible anyway. Dr. Jones Physics 280 antum Mechanics Lecture Einstein takes this result at face value and shows that photons are quantized in the same way, explaining the photoelectric eect. Bohr adapts the idea of quantization to ”explain” the Rydberg equation and why the emission/absorption spectrum is quantized. He quantizes angular momentum. Review of Early antum Mechanics Formalization of antum Mechanics So far.. Electrical charges are quantized in the form of electrons and protons, nothing is smaller than ±e. Classical Physics predicts that the intensity of radiation from blackbody-like sources goes to infinity with decreasing wavelength, which is experimentally shown to be untrue and is impossible anyway. Planck uses a mathematical trick for the first time ever–energy quantization: E = hf to ”fix” the equations. Dr. Jones Physics 280 antum Mechanics Lecture Bohr adapts the idea of quantization to ”explain” the Rydberg equation and why the emission/absorption spectrum is quantized. He quantizes angular momentum. Review of Early antum Mechanics Formalization of antum Mechanics So far.. Electrical charges are quantized in the form of electrons and protons, nothing is smaller than ±e. Classical Physics predicts that the intensity of radiation from blackbody-like sources goes to infinity with decreasing wavelength, which is experimentally shown to be untrue and is impossible anyway. Planck uses a mathematical trick for the first time ever–energy quantization: E = hf to ”fix” the equations. Einstein takes this result at face value and shows that photons are quantized in the same way, explaining the photoelectric eect. Dr. Jones Physics 280 antum Mechanics Lecture Review of Early antum Mechanics Formalization of antum Mechanics So far.. Electrical charges are quantized in the form of electrons and protons, nothing is smaller than ±e. Classical Physics predicts that the intensity of radiation from blackbody-like sources goes to infinity with decreasing wavelength, which is experimentally shown to be untrue and is impossible anyway. Planck uses a mathematical trick for the first time ever–energy quantization: E = hf to ”fix” the equations. Einstein takes this result at face value and shows that photons are quantized in the same way, explaining the photoelectric eect. Bohr adapts the idea of quantization to ”explain” the Rydberg equation and why the emission/absorption spectrum is quantized. He quantizes angular momentum. Dr. Jones Physics 280 antum Mechanics Lecture Review of Early antum Mechanics Formalization of antum Mechanics A new truth Energy is quantized. Dr. Jones Physics 280 antum Mechanics Lecture We use blackbody radiation as a proxy for the more complex thermal radiation. Wien’s law can explain the shi of the peak lewards with temperature. −2 λmax T = 0:2898 × 10 mK Review of Early antum Mechanics Formalization of antum Mechanics The Ultraviolet Catastrophe Thermal radiation of a body depends upon the temperature and wavelength. Dr. Jones Physics 280 antum Mechanics Lecture Wien’s law can explain the shi of the peak lewards with temperature. −2 λmax T = 0:2898 × 10 mK Review of Early antum Mechanics Formalization of antum Mechanics The Ultraviolet Catastrophe Thermal radiation of a body depends upon the temperature and wavelength. We use blackbody radiation as a proxy for the more complex thermal radiation. Dr. Jones Physics 280 antum Mechanics Lecture Review of Early antum Mechanics Formalization of antum Mechanics The Ultraviolet Catastrophe Thermal radiation of a body depends upon the temperature and wavelength. We use blackbody radiation as a proxy for the more complex thermal radiation. Wien’s law can explain the shi of the peak lewards with temperature. −2 λmax T = 0:2898 × 10 mK Dr. Jones Physics 280 antum Mechanics Lecture Review of Early antum Mechanics Formalization of antum Mechanics Why we can approximate some glowing bodies as blackbody radiation Dr. Jones Physics 280 antum Mechanics Lecture Combining these laws yields the Rayleigh-Jeans prediction: 2πck T I(λ, T) = B λ4 Classical physics could take us no further, and it was wrong. Review of Early antum Mechanics Formalization of antum Mechanics The Ultraviolet Catastrophe Stefan’s law predicts the power emied by blackbody radiation: P = σAeT 4 Dr. Jones Physics 280 antum Mechanics Lecture Classical physics could take us no further, and it was wrong. Review of Early antum Mechanics Formalization of antum Mechanics The Ultraviolet Catastrophe Stefan’s law predicts the power emied by blackbody radiation: P = σAeT 4 Combining these laws yields the Rayleigh-Jeans prediction: 2πck T I(λ, T) = B λ4 Dr. Jones Physics 280 antum Mechanics Lecture Review of Early antum Mechanics Formalization of antum Mechanics The Ultraviolet Catastrophe Stefan’s law predicts the power emied by blackbody radiation: P = σAeT 4 Combining these laws yields the Rayleigh-Jeans prediction: 2πck T I(λ, T) = B λ4 Classical physics could take us no further, and it was wrong. Dr. Jones Physics 280 antum Mechanics Lecture n is a positive integer, the quantum number, f is frequency of vibration, h is a new constant he fit to experimental results: h = 6:626 × 10−34J · s 2πhc2 I(λ, T) = hc λ5 e λkBT − 1 Review of Early antum Mechanics Formalization of antum Mechanics The Ultraviolet Catastrophe: Resolved Reluctantly Planck’s leap: Supposing that blackbody radiation was emied by ’resonators’, these resonators could only have energy in discreet quantity: En = nhf Dr. Jones Physics 280 antum Mechanics Lecture 2πhc2 I(λ, T) = hc λ5 e λkBT − 1 Review of Early antum Mechanics Formalization of antum Mechanics The Ultraviolet Catastrophe: Resolved Reluctantly Planck’s leap: Supposing that blackbody radiation was emied by ’resonators’, these resonators could only have energy in discreet quantity: En = nhf n is a positive integer, the quantum number, f is frequency of vibration, h is a new constant he fit to experimental results: h = 6:626 × 10−34J · s Dr. Jones Physics 280 antum Mechanics Lecture Review of Early antum Mechanics Formalization of antum Mechanics The Ultraviolet Catastrophe: Resolved Reluctantly Planck’s leap: Supposing that blackbody radiation was emied by ’resonators’, these resonators could only have energy in discreet quantity: En = nhf n is a positive integer, the quantum number, f is frequency of vibration, h is a new constant he fit to experimental results: h = 6:626 × 10−34J · s 2πhc2 I(λ, T) = hc λ5 e λkBT − 1 Dr. Jones Physics 280 antum Mechanics Lecture Another mystery dominated atomic physics–nobody