Cold collisions: chemistry at ultra-low temperatures; in: Tutorials in molecular
... where kB is the Boltzmann constant and A is a proportionality constant. The activation energy E A is the energy required to pass the transition state. The expression can be derived using classical statistical mechanics. It predicts that the reaction rate drops to zero quickly when kB T Ea . Some r ...
... where kB is the Boltzmann constant and A is a proportionality constant. The activation energy E A is the energy required to pass the transition state. The expression can be derived using classical statistical mechanics. It predicts that the reaction rate drops to zero quickly when kB T Ea . Some r ...
Assignment 6
... e) Substitute in these forms for the integrals to get a function for the expected ground state electronic energy. Use Mathematica or whatever package you like to plot this energy function versus Z and R. Choose some appropriate energy scale to make the energy function dimensionless; make sure you st ...
... e) Substitute in these forms for the integrals to get a function for the expected ground state electronic energy. Use Mathematica or whatever package you like to plot this energy function versus Z and R. Choose some appropriate energy scale to make the energy function dimensionless; make sure you st ...
The Schrödinger Equations
... (where x0 is a constant) is satisfied by the delta function δ(x − x0 ). (The equation must be satisfied for all x, but it is: check it separately for x = x0 and x 6= x0 .) The operator for any function of x is simply (to multiply by) that function; in particular, the potential energy operator is sim ...
... (where x0 is a constant) is satisfied by the delta function δ(x − x0 ). (The equation must be satisfied for all x, but it is: check it separately for x = x0 and x 6= x0 .) The operator for any function of x is simply (to multiply by) that function; in particular, the potential energy operator is sim ...
Singlet±triplet transitions in a few
... transition. The electro-chemical potential of a dot containing N electrons is de®ned as l N U N ÿ U N ÿ 1 where U N is the total energy of the dot. For an N 1 dot, U " 1 E0;0 is the exact ground state energy (spins are indicated by arrows). In the CI model, U "# 2 2E0;0 Ec , ...
... transition. The electro-chemical potential of a dot containing N electrons is de®ned as l N U N ÿ U N ÿ 1 where U N is the total energy of the dot. For an N 1 dot, U " 1 E0;0 is the exact ground state energy (spins are indicated by arrows). In the CI model, U "# 2 2E0;0 Ec , ...
Momentum vs. Wavevector
... • States like |x0〉 and |k0〉 have 〈ψ|ψ〉=∞ • All physical states must have 〈ψ|ψ〉=1 • CONCLUSION 1: states such as |x0〉 and |k0〉 are non-physical, and can therefore only be used as intermediate states in calculations • CONCLUSION 2: Since a measurement of X produces the nonphysical state |x0〉, such a x ...
... • States like |x0〉 and |k0〉 have 〈ψ|ψ〉=∞ • All physical states must have 〈ψ|ψ〉=1 • CONCLUSION 1: states such as |x0〉 and |k0〉 are non-physical, and can therefore only be used as intermediate states in calculations • CONCLUSION 2: Since a measurement of X produces the nonphysical state |x0〉, such a x ...
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.