Lecture XV
... • A real eigenvalue means that the physical quantity for which the operator stands for can be measured experimentally. • The eigenvalues of two commuting operators can be computed by using the common set of eigenfunctions. If the two operators commute, then it is possible to measure the simultaneous ...
... • A real eigenvalue means that the physical quantity for which the operator stands for can be measured experimentally. • The eigenvalues of two commuting operators can be computed by using the common set of eigenfunctions. If the two operators commute, then it is possible to measure the simultaneous ...
Chapter 9: Electrons in Atoms
... by the symbol Y. ~ When the equation is solved for a particle, it is found that the wavefunction has a wavelength given by de Broglie relation, and that solutions of the equation exist for any wavelength. ~ However when the equation is solved for a particle in a confined small region or is bound to ...
... by the symbol Y. ~ When the equation is solved for a particle, it is found that the wavefunction has a wavelength given by de Broglie relation, and that solutions of the equation exist for any wavelength. ~ However when the equation is solved for a particle in a confined small region or is bound to ...
Lecture 15 Summary
... thermodynamics. In equilibrium, the net energy transfer comes to an end, and the temperatures equalize. In analogy, we would like to define a ‘potential’ that determines how particles move from one system to another when they are brought into contact. We shall term the exchange of particles between ...
... thermodynamics. In equilibrium, the net energy transfer comes to an end, and the temperatures equalize. In analogy, we would like to define a ‘potential’ that determines how particles move from one system to another when they are brought into contact. We shall term the exchange of particles between ...
... When electrons are confined to a small region of a semiconductor they form a quantum dot, and the energy and the charge on the quantum dot are quantized. It has been possible to study the transmission of electrons through a quantum dot by coupling the states in the dot to external leads via a tunnel ...
Document
... The trajectory of a particle scattered by a spherically symmetric potential fly) is determined in the classical approximation by two parameters, e.g., the particle velocity v, a t infinity and the impact parameter b, o r else the total energy E and the angular momentum I. The deflection angle x is a ...
... The trajectory of a particle scattered by a spherically symmetric potential fly) is determined in the classical approximation by two parameters, e.g., the particle velocity v, a t infinity and the impact parameter b, o r else the total energy E and the angular momentum I. The deflection angle x is a ...
Appendix D Wigner Function Formulation of Gross
... corresponding wavefunction dynamics are governed by the Gross-Pitaevskii equation, in fairly complete detail compared to Appendix 11.A of the preprint in the previous Chapter. We find that this equation of motion can be written as a sum of terms multiplied by powers of , corresponding to the case fo ...
... corresponding wavefunction dynamics are governed by the Gross-Pitaevskii equation, in fairly complete detail compared to Appendix 11.A of the preprint in the previous Chapter. We find that this equation of motion can be written as a sum of terms multiplied by powers of , corresponding to the case fo ...
“What is quantum theory about?” Jos Uffink March 26, 2010, Utrecht
... where Sd is the single-particle state space, and P(ρ) some probability density over Sd . ...
... where Sd is the single-particle state space, and P(ρ) some probability density over Sd . ...
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.