Lectures 3-5
... •Waves are characterized by several interrelated properties: – wavelength (λ): the distance between successive crests or successive troughs – frequency (ν): the number of waves passing through a point in a given period of time – amplitude (A): the height of a wave (from the node) – Speed (c for ligh ...
... •Waves are characterized by several interrelated properties: – wavelength (λ): the distance between successive crests or successive troughs – frequency (ν): the number of waves passing through a point in a given period of time – amplitude (A): the height of a wave (from the node) – Speed (c for ligh ...
on the behaviour of atoms in an electromagnetic wa ve field
... in the »differences« by which the classical differentials were replaced, disappear; a feature which illustrates very clearly the profound difference between the quantum theory of atoms and the classical theory of electrons. Formally, the formula thus obtained for the scattering momentum in the norma ...
... in the »differences« by which the classical differentials were replaced, disappear; a feature which illustrates very clearly the profound difference between the quantum theory of atoms and the classical theory of electrons. Formally, the formula thus obtained for the scattering momentum in the norma ...
Document
... • Electrons are not ejected for frequencies below f0. • Electrons have a probability to be emitted immediately. Conclusions: • Light arrives in “packets” of energy (photons). • Ephoton = hf ← We will see that this is valid for all objects. It is the fundamental QM connection between an object’s wave ...
... • Electrons are not ejected for frequencies below f0. • Electrons have a probability to be emitted immediately. Conclusions: • Light arrives in “packets” of energy (photons). • Ephoton = hf ← We will see that this is valid for all objects. It is the fundamental QM connection between an object’s wave ...
Quantum-to-classical transition for fluctuations in the early Universe
... The momentum is always a QND variable for the free particle, but for large times also position becomes such a variable, since [x̂(t2 ), x̂(t1 )] ≈ 0, like (8) above. Note that for a different but closely related experiment when we fix some large value of x and measure the arrival time of a particle ...
... The momentum is always a QND variable for the free particle, but for large times also position becomes such a variable, since [x̂(t2 ), x̂(t1 )] ≈ 0, like (8) above. Note that for a different but closely related experiment when we fix some large value of x and measure the arrival time of a particle ...
Waves and Energy
... did not address the question of why the negatively charged electrons are not pulled into the atom's positively charged nucleus. ...
... did not address the question of why the negatively charged electrons are not pulled into the atom's positively charged nucleus. ...
Physics 2170
... E g u mc2 B. The proton and pion have the same energy Erest mc2 but the proton has more momentum. C. The proton and pion have the same E2 ( pc)2 (mc2)2 momentum but the proton has more energy. D. The proton and pion have equal and opposite pc / E momenta and the proton has more energy. E ...
... E g u mc2 B. The proton and pion have the same energy Erest mc2 but the proton has more momentum. C. The proton and pion have the same E2 ( pc)2 (mc2)2 momentum but the proton has more energy. D. The proton and pion have equal and opposite pc / E momenta and the proton has more energy. E ...
Transcript of Speech by Professor Stephen Hawking
... weather forecasts are so unreliable. Despite these practical difficulties, scientific determinism, remained the official dogma throughout the 19th century. However, in the 20th century, there have been two developments that show that Laplace's vision, of a complete prediction of the future, can not ...
... weather forecasts are so unreliable. Despite these practical difficulties, scientific determinism, remained the official dogma throughout the 19th century. However, in the 20th century, there have been two developments that show that Laplace's vision, of a complete prediction of the future, can not ...
We now extend the trace distance and fidelity to the quantum case
... We’ve encountered some quantum operations, including unitary operation and orthogonal measurements. One can of course have other operations, such as adding a quantum system and discarding part of a system. In general, one can use arbitrary sequence of the above operations to an existing system A, su ...
... We’ve encountered some quantum operations, including unitary operation and orthogonal measurements. One can of course have other operations, such as adding a quantum system and discarding part of a system. In general, one can use arbitrary sequence of the above operations to an existing system A, su ...
Lecture 1
... the detector attended by a flash near hole 1 and hole 2, respectively. In column 3 we record those electrons which reached the detector without producing a flash. The data in columns 1 and 2 give rise to the probability distributions P1 and P2 . But the data in column 3 which correspond to unseen ...
... the detector attended by a flash near hole 1 and hole 2, respectively. In column 3 we record those electrons which reached the detector without producing a flash. The data in columns 1 and 2 give rise to the probability distributions P1 and P2 . But the data in column 3 which correspond to unseen ...
Particle in a box
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example a ball trapped inside a large box, the particle can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never ""sit still"". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.The particle in a box model provides one of the very few problems in quantum mechanics which can be solved analytically, without approximations. This means that the observable properties of the particle (such as its energy and position) are related to the mass of the particle and the width of the well by simple mathematical expressions. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.