#### 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#### Mechanical Problems With Second Order Differential Equations

Many problems in mechanics gives rise to second order differential equations as a consequence of Newton's second law of motion, The acceleration a is actually the second differential of position with respect to time, so any problem involing...

https://astarmathsandphysics.com/a-level-maths-notes/m5/3669-mechanical-problems-with-second-order-differential-equations.html#### Mechanism of X - Ray Attenuatino

When an X – ray hits a material, it generally penetrates the material and it's energy is gradually reduced as it passes through the matter. There are several mechanisms via which this may happen, summarised in the table below. Note that = attenuation...

https://astarmathsandphysics.com/a-level-physics-notes/electrons-and-photons/2660-mechanism-of-x-ray-attenuatino.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#### 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#### 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 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#### 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#### Bohr's Model of the Hydrogen Atom

of angular momentum in units of where This means we can write We can use the ordinary rules of classical Newtonian mechanics to derive the equation giving the differences in the energy levels of the electrons in the Hydrogen atom. We can equate the...

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1646-bohr-s-model-of-the-hydrogen-atom.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#### The Paul Exclusion Principle

possess an intrinsic angular momentum whose value is times a half-integer (1/2, 3/2, 5/2, etc.). In the theory of quantum mechanics, fermions are described by "antisymmetric states" such that if any two are interchanged, a phase change in the...

https://astarmathsandphysics.com/university-physics-notes/quantum-mechanics/1652-the-paul-exclusion-principle.html