Physics in Ultracold atoms
... World of zero temperature --- introduction to systems of ultracold atoms Daw-Wei Wang National Tsing-Hua University ...
... World of zero temperature --- introduction to systems of ultracold atoms Daw-Wei Wang National Tsing-Hua University ...
Final
... the superconductor. Assuming ∆ ¿ ²F , find the approximate wavefunctions on the normal and superconducting sides, using continuity. [13 mks] (5) Consider the Hamiltonian for an electron system with a 2-body interaction P P p2 † ap ap + p1 ,p2 ,q qvn a†p1 +q a†p2 −q ap2 ap1 , H = p 2m where v is some ...
... the superconductor. Assuming ∆ ¿ ²F , find the approximate wavefunctions on the normal and superconducting sides, using continuity. [13 mks] (5) Consider the Hamiltonian for an electron system with a 2-body interaction P P p2 † ap ap + p1 ,p2 ,q qvn a†p1 +q a†p2 −q ap2 ap1 , H = p 2m where v is some ...
Document
... • A determinant changes sign when two rows (or columns) are exchanged. “antisymmetric” Exchanging two electrons leads to a change in sign of the wave function. ...
... • A determinant changes sign when two rows (or columns) are exchanged. “antisymmetric” Exchanging two electrons leads to a change in sign of the wave function. ...
May 2003
... One can manipulate the spin state of the particle by subjecting it to a time-dependent field B B1 (cos(φ(t)), sin(φ(t)), 0) that rotates in the x-y plane at a variable frequency φ̇(t). We will discuss different ways of choosing φ(t) to achieve the goal transforming an initial Sz = −1/2 state into an ...
... One can manipulate the spin state of the particle by subjecting it to a time-dependent field B B1 (cos(φ(t)), sin(φ(t)), 0) that rotates in the x-y plane at a variable frequency φ̇(t). We will discuss different ways of choosing φ(t) to achieve the goal transforming an initial Sz = −1/2 state into an ...
Classical Particles Having Complex Energy Exhibit Quantum
... behavior endlessly but at no point does the trajectory cross itself. This classicalparticle motion is analogous to the behavior of a quantum particle that repeatedly tunnels between two classically allowed regions. Here, the particle does not disappear into the classically forbidden region during th ...
... behavior endlessly but at no point does the trajectory cross itself. This classicalparticle motion is analogous to the behavior of a quantum particle that repeatedly tunnels between two classically allowed regions. Here, the particle does not disappear into the classically forbidden region during th ...
2. Many-electron systems
... Wave function: constructed from the occupied orbitals by a product (Hartree) or as a determinant (Hartree-Fock); the occupied orbitals are selected according to the increasing value of the orbital energy (so called Aufbau principle). Some important terms: • Shell: collection of the orbitals with the ...
... Wave function: constructed from the occupied orbitals by a product (Hartree) or as a determinant (Hartree-Fock); the occupied orbitals are selected according to the increasing value of the orbital energy (so called Aufbau principle). Some important terms: • Shell: collection of the orbitals with the ...
chemical identity and structure
... • Quantum mechanics acknowledges the wave-particle duality of matter by supposing that, rather than travelling a definite path, a particle is distributed through space like a wave. The mathematical representation of the wave that in quantum mechanics replaces the classical concept of trajectory is c ...
... • Quantum mechanics acknowledges the wave-particle duality of matter by supposing that, rather than travelling a definite path, a particle is distributed through space like a wave. The mathematical representation of the wave that in quantum mechanics replaces the classical concept of trajectory is c ...
6.2 Growth and structure of semiconductor quantum wells
... heavy hole transition at 1.59 eV. This is closely followed by the step due to the n = 1 light hole transition at 1.61eV. The steps at the band edge are followed by a flat spectrum up to 1.74 e. At 1.77 eV there is a further step due to the onset of the n = 2 heavy hole transition, then n = 3 at 2.03 ...
... heavy hole transition at 1.59 eV. This is closely followed by the step due to the n = 1 light hole transition at 1.61eV. The steps at the band edge are followed by a flat spectrum up to 1.74 e. At 1.77 eV there is a further step due to the onset of the n = 2 heavy hole transition, then n = 3 at 2.03 ...
S.V. Stepanov
... small finite 3d-potential well. In such cavities Ps cannot be bound, it does not exert any repulsive pressure on them and does not stimulate their transformation into equilibrium Ps bubble. It could be that finding a suitable preexisting cavity, where qf-Ps may localize, be a limiting factor of form ...
... small finite 3d-potential well. In such cavities Ps cannot be bound, it does not exert any repulsive pressure on them and does not stimulate their transformation into equilibrium Ps bubble. It could be that finding a suitable preexisting cavity, where qf-Ps may localize, be a limiting factor of form ...
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.