#### Some Strange Implications of Quantum Mechanics

Quantum m,echanics can have some very strange implications. A particle may be in several places at one. This is a consequence of the state of the particle being described by a wavefunction, with the probability of a particle being in a region of space...

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1641-some-strange-implications-of-quantum-mechanics.html#### The Connectin Between Kinetic Energy in Newtonian and Relativistic Mechanics

In Newtonian mechanics, the momentum and kinetic energy are given by and The relationship between momentum p and kinetic energy is often written as Many equations and concepts in Newtonian mechanics have close analogies in special relativity. For...

https://astarmathsandphysics.com/ib-physics-notes/relativity/1446-the-connectin-between-kinetic-energy-in-newtonian-and-relativistic-mechanics.html#### Quantum Mechanical Operators

and dymamics can be described with the deterministic equations of Newtonian physics. Part of the development of quantum mechanics is the establishment of the operators associated with the parameters needed to describe the system. Some of those operators...

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1637-quantum-mechanical-operators.html#### Mechanical Determinism

Newtonian mechanics is a complete system. Given a state of a system of particles and the mass, velocity and position of each particle, the state of the system – the position and velocity of each particle can be determined at any subsequent or previous...

https://astarmathsandphysics.com/ib-physics-notes/the-history-and-development-of-physics/1317-mechanical-determinism.html#### The Mechanics of Atomic Spectra

In an atom, electrons occupy orbits, each with a particular energy. The orbits and energies are specific to each element. This energy is negative because the electron and nucleus are oppositely charged, so attract each other and energy must be given to...

https://astarmathsandphysics.com/ib-physics-notes/atomic-and-nuclear-physics/1230-the-mechanics-of-atomic-spectra.html#### The Mechanism of Lightning Production

Static electricity is commonly produced when insulating materials rub together. When fur is rubbed against an ebonite rod, the fur becomes negatively charged and the rod becomes positively charged. Electrons are transferred from one material to the rod...

https://astarmathsandphysics.com/o-level-physics-notes/261-the-mechanism-of-lightning-production.html#### The Mechanism of Light Production by a Gas Discharge Tube

Gas is normally not a good conductor of electricity. The molecules of the gas are electrically neutral and the gas contains very few ions. This means that in order for a gas to conduct electricity, a source of electrons is needed. In a gas discharge...

https://astarmathsandphysics.com/o-level-physics-notes/262-the-mechanism-of-light-production-by-a-gas-discharge-tube.html#### Principle of Least Action

principle that can be used to obtain the equations of motion for that system in a way that is independent of Newtonian mechanics. The action principle is preceded by earlier ideas in surveying and optics. The rope stretchers of ancient Egypt stretched...

https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/1530-principle-of-least-action.html#### Postulates

to 1. Thewavefunction must be single-valued, continuous, and finite. Postulate 2. To every observable in classical mechanics therecorresponds a linear, Hermitian operator in quantum mechanics.If we require that the expectation value of an operator...

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1634-postulates.html#### The Born Interpretation

The fundamental equation of quantum mechanics is the Schroedinger equation. It was introduced as a wave equation which did not contradict the relation between the energy and the momentum of a particle in classical mechanics. As a result, the wave...

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1647-the-born-interpretation.html#### The Einstein Rosen Podolsky Experiment

other. We have a source that emits electron-positron pairs, with the electron sent to destination A. According to quantum mechanics, we can arrange our source so that each emitted pair occupies a quantum state called a spin singlet. This can be viewed...

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1649-the-einstein-rosen-podolsky-experiment.html#### Angular Momentum Operators and Commutation Relations in Quantum Physics

In is one of the fundamental differences of quantum physics with classical mechanics that in the quantum world we cannot know all measurements to absolute precision. Some quantities 'pair up' so absolute knowledge of one precludes absolute knowledge of...

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1625-angular-momentum-operators-and-commutation-relations-in-quantum-physics.html#### The Schrodinger Equation

The general equation expressing the conservation of energy of a particle in classical mechanics is In quantum mechanics we have something very similar, with the intoduction of a concept called the wavefunction. or equivalently The first of these is...

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1653-the-schrodinger-equation.html#### Definitions

Terms commonly used everyday by ordinary people may have a slightly different meaning in physics. Many people for example confuse velocity and speed. These are not the same, the difference being that velocity is the speed of a body in a certain...

https://astarmathsandphysics.com/ib-physics-notes/mechanics/1356-definitions.html#### Introduction to Angle Action Variables

taken together are called angle action variables. Angle action variables are of fundamental importance in quantum mechanics, where they are used for example to model the radiation emitted from quantum systems. Most Hamiltonians for functions of both the...

https://astarmathsandphysics.com/university-physics-notes/classical-mechanics/1524-introduction-to-angle-action-variables.html#### The Cauchy - Riemann Equations

of the velocity field of a steady incompressible, irrotational flow in two dimensions. The equations are occur in fluid mechanics from consideration of the velocity potential and are found from the velocity potential The condition that the flow be...

https://astarmathsandphysics.com/university-physics-notes/fluid-mechanics/1563-the-cauchy-riemann-equations.html#### Angular Momentum Operators

momentum is so important because it is conserved in any isolated system. The same relationship, (1) holds in quantum mechanics, with and being the position and momentum operators respectively: can be evaluated as the determinant of a matrix, the first...

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1624-angular-momentum-operators.html#### Expectation Values

value between certain limits the we evaluate an integral. In this case where the range of possible values is In quantum mechanics we have something similar. Remember that the probability density of a particle is given by where is the operator of the...

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1628-expectation-values.html#### Quantum Tunnelling

0 in region III there is a non zero probability of finding the particle in region III, which is forbidden by classical mechanics since it has insufficient energy to surmount the barrier.

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1638-quantum-tunnelling.html#### Reflection From a Potential Barrier

it is not automatically relected, even if it has insufficient energy to over come the barrier according to classical mechanics. If the potential barrier has finite height, the wavefunction partially penetrates the barrier. If the barrier has finite...

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1639-reflection-from-a-potential-barrier.html