Simply Lecture

A chain of title is defined as the historical transfers of  ownership title towards a property. It is a valuable tool that show the past owners of a property and serves as a property's historical ownership title.  For better understanding, chain of title simply refers to a document showing the past owners of a property to the present. For example, a land that was owned by Mr. John Bally was sold to Mr. Cam You in the year 1942, later on Mr. Cam You sold it to Mr. First Born in the year 1972 which is presently the owner of the property. The chain of title, is the successive sequence of the documentation of the historical owners to the present; that is: Mr. John Bally (landlord 1920-1942), Mr. Cam You (landlord 1942-1972) and Mr. First Born (landlord 1972-till date). Chain of title is a legal document, and so it is maintained by a registry office or civil law notary. Chain of title for real estate or property  Real estate are one of the field were the chain of title is taking mo

Angel flight is a term used by group of people whose members are provided with free air transportation,  because they are in need with free medical treatment far from home. The transportation of passengers are done by volunteer pilots using their own general aviation aircraft. History of angel flight  The first two organisation to be termed "angel flight" was founded in the year 1983. The first organisation was formed in Santa Monica, California known as the "Angel flight of California (presently Angel Flight West)". The second was formed in Atlanta, Georgia and was called "Angel Flight Soars" Accidents and incidents On 15th August, 2011 a Piper PA-28 Cherokee conducting an angel flight crashed in rural Victoria, Australia. On May 24, 2013 an angel flight crashed into a pond in Ephratah, New York. On June 28, 2017 a TBIO Tobago serving an angel flight crashed into a terrain near MT Gambier heading to Adelaide. Pilots  The pilots of angel flig

A panfish is a kind of fish (usually pursued by recreational anglers) that do not out grow the size of a frying pan. It is a term used by recreational anglers for small fish which could fit into a pan, but it is edible and legal for eating. Example of a pan fish. Species of the panfish  Bluegill (Lepomis machrochirus)  Green sunfish (Lepomis cyanellus)  Redear sunfish (Lepomis microlophus)  Redbreast sunfish (Lepomis auritus)  Spotted sunfish (Lepomis punctatus)  Pumpkinseed (Lepomis gibbosus)  Warmouth (Chaenobryttus gulosus)  The size of a pan fish  However, it is stated above that the size of the panfish is a fish that takes the size of a frying pan. But a typical size of the bluegill exist which is about 4 to 12 inches and has  a maximum size of 16 inches. The largest bluegill ever existed was caught in the year 1950, with an average size of about 4 pounds (12 ounces).

What is the halo effect?  The halo effect is a kind of cognitive bias, that make one part of someone seems more attractive or desirable. This concept can be applied to people, product, brand, business etc.  The halo effect can also be seen as the final judgment of someone towards a person, product, brand, business etc. by their first impression without serious information. For example, if John is working in an office where you work; and you see John as creative guy and someone ask you, "please, do you know someone who can decorate my room?". You will simply recommend John because you think that John is creative. From the above example, you choose John not because you have actually investigated if John can actually decorate a room,  but because you feel that John is creative and could be able to decorate a room.  The halo effect usually refers to when the judgment of the behavior is positive, otherwise if negative it is refer to as "horn effect" How halo e

What is cyanide? Cyanide is a chemical compound that consist of carbon (C) and nitrogen (N). It exist in different forms, so we can say; sodium cyanide, hydrogen cyanide, potassium cyanide and others. Most of these variants (forms of cyanide) are poisonous, that in can cause death within minutes. The origin of cyanide, started from the fact that a huge number of Nazi uses the potassium cyanide suicide pills to kill themselves during the World War II. The most dangerous form of cyanide is the hydrogen cyanide, which is in the form of gas; and is deadly when inhaled. Uses of cyanide  Despite the horrible fact of cyanide as  a poison, cyanide has its own importance as it is useful.  The uses of cyanide include: I. It is used in industrial chemistry, in the production of nylon. II. It is used for pest control, bring the key ingredient in the poison used to kill animals, such as rats and other rodents. III. It is used in the mining of golds and silver, to be able to dissolve these

The Schrodinger equation in quantum mechanics, is a mathematical equation that describes the change over time of a physical system in which quantum effects,  such as wave-particle duality, are significant. The equation is a mathematical formulation for studying quantum mechanical systems. It is used to find the allowed energy levels of the quantum mechanical system (atoms, or transistors). The associated wave function gives the probability of finding the particle at a certain position. The Schrodinger equation exist in different forms: I.  Energy form of Schrodinger equation: $$\frac{E^{2}}{2m} = E - V(r)$$ II. The time independent Schrodinger equation: $$-\frac{\hbar^{2}}{2m} \nabla^{2} \psi(r) + V(r) \psi(r) = E \psi(r)$$ III.  Time dependent Schrodinger equation: $$-\frac{\hbar^{2}}{2m} \nabla^{2} \Psi(r,t) + V(r) \Psi(r,t) = i\hbar \frac{d\Psi(r,t)}{dt}$$ IV.  Auxiliary time dependent Schrodinger equation: $$-\frac{\hbar^{2}}{2m} \nabla^{2} \Psi(r,t) + V(r) \Psi(r,t) = -i

The unified theory of wave-particle duality has been used to derive the Schrödinger equations. The Schrodinger equations are generally accepted, by postulate rather than derivation, to be laws of physics. The Schrodinger equations provide a basis for analyzing many kinds of systems (molecular, atomic, and nuclear) in a particular inertial reference frame. The success of the Schrödinger equations constitutes a basis for accepting them, their derivations, and the unified theory of wave-particle duality which makes such derivations possible. This acceptance is completely justified in the favored inertial reference frame. In accord with the principle of relativity, all physical laws must be the same in all inertial reference frames, i.e., all physical laws must be Lorentz invariant. Recall, the relationship: $$\nabla^{2} \psi = \frac{\partial^{2} \psi}{\partial t^{2}}$$ ...........(1) Equ (1) is Lorentz invariant and reduces, by means of the procedure presented in the previou

Recall the relationship: $$\phi(t) = C_+ exp[-i(\frac{E}{\hbar})t] + C_- exp[i(\frac{E}{\hbar})t]$$ .............(1) Recall, from the present special case: $$C_+ = 0$$ ........(2) Substitute equ (2) into equ (1), we have that: $$\phi(t) = C_- exp[i(\frac{E}{\hbar})t]$$ .......(3) Also,  recall the relationship: $$\Psi(r,t) = \psi(r) \phi(t)$$ ..........(4) Substitute equ (3) into equ (4): $$\Psi(r,t) = C_- exp \psi (r)  [i(\frac{E}{\hbar})t]$$ ..............(5) Equ (5) can be differentiated with respect to t, and by rearranging we have: $$\Psi(r,t) = -i(\frac{\hbar}{E}) \frac{d \Psi (r, t)}{dt}$$ ..............(6) Recall the relationship: $$-\frac{\hbar^{2}}{2m} \nabla^{2} \Psi(r,t) + V(r) \Psi(r,t) = E \Psi(r,t)$$ ...........(7) Substituting equ (6) into the right hand side of equ (7) we have: $$-\frac{\hbar^{2}}{2m} \nabla^{2} \Psi(r,t) + V(r) \Psi(r,t) = i\hbar \frac{d \Psi(r,t)}{dt}$$ .........(8) Equ (8) is the auxiliary time dependent Schrodinger equation

Recall the relationship: $$k = \frac{E}{\hbar}$$ ........(1) And also the relationship: $$(\nabla^{2} + k^{2}) \psi (r)=0$$ ........(2) Substitute equ (1) into equ (2) $$(\nabla^{2} + \frac{E^{2}}{\hbar^{2}}) \psi (r) = 0$$ Opening the brackets: $$\nabla^{2} \psi(r) + \frac{E^{2}}{\hbar^{2}} \psi(r) =0$$ Therefore: $$\nabla^{2} \psi(r) = -(\frac{E}{\hbar})^{2} \psi(r)$$ ............(3) Multiply both sides of equ (3) by \(-\frac{\hbar^{2}}{2m}\), we have: $$-\frac{\hbar^{2}}{2m} \nabla^{2} \psi(r) = \frac{\hbar^{2}}{2m} (\frac{E^{2}}{\hbar^{2}}) \psi(r)$$ $$-\frac{\hbar^{2}}{2m} \nabla^{2} \psi(r) = (\frac{E^{2}}{2m}) \psi(r)$$ ..........(4) Recall, the relationship from the energy form of the Schrodinger equation, we have: $$\frac{E^{2}}{2m} = E - V(r)$$ .............(5) Substitute equ (5) into equ (4): $$-\frac{\hbar^{2}}{2m} \nabla^{2} \psi(r) = (E - V(r)) \psi(r)$$ Opening bracket,  we have: $$-\frac{\hbar^{2}}{2m} \nabla^2 \psi (r) = E \psi (r) - V(r) \psi (r)$$

Recall from the time independent Schrodinger equation: $$-\frac{\hbar^{2}}{2m} \nabla^{2} \psi(r) + V(r) \psi(r) = E \psi(r)$$ ........(1) Multiply both sides of equ (1) by \(\phi(t)\), we have: $$-\frac{\hbar^{2}}{2m} \nabla^{2} \psi(r) \phi(t) + V(r) \psi(r) \phi(t) = E \psi(r) \phi(t)$$ ..........(2) Recall: $$\psi(r) \phi(t) = \Psi(r,t)$$ .............(3) Substitute equ (3) into equ (2): $$-\frac{\hbar^{2}}{2m} \nabla^{2} \Psi(r,t) + V(r) \Psi(r,t) = E \Psi(r,t)$$ .........(4) Recall that the well known Planck-Einstein relation is given by: $$E = hv$$ ...........(5) And also, the reduced Planck's constant is given by: $$\hbar = \frac{h}{2\pi}$$ ................(6) Also recall that time dependence is given by: $$\phi(t) = C_+ exp(-i2\pi vt) + C_- exp(i2\pi vt)$$ ..........(7) Substituting equ (6) into (5), we have: $$V = \frac{E}{\hbar 2 \pi}$$ ..........(8) Substitute equ (8) into equ (7) $$\phi(t) = C_+ exp(-i2 \pi \frac{E}{\hbar 2 \pi} t)  + C_- exp(i2 \pi \f

Recall that classical energy is given by the equation: $$E_c = \frac{p^{2}}{2m} + V(r) + V_0$$ ........(1) Where, V( r ) = spatially dependent potential              \(V_0\) = constant potential energy Recall from the square of the magnitude of the momenergy 4-vector associated with quantum object is given by: $$E^{2} - p^{2} = m^{2}$$ ..........(2) Divide equ (2) by 2m $$\frac{E^{2}}{2m} - \frac{p^{2}}{2m} = \frac{m^{2}}{2m}$$ $$\frac{E^{2}}{2m} - \frac{p^{2}}{2m} = \frac{m}{2}$$ Making \(\frac{p^{2}}{2m}\) subject of the formula, we have: $$\frac{p^{2}}{2m} = \frac{E^{2}}{2m} - \frac{m}{2}$$ .........(3) Also let: $$V_0 = \frac{m}{2} + E_c - E$$ ............(4) Substitute equ (4) and equ (3) into equ (1), we have: $$E_c = \frac{E^{2}}{2m} - \frac{m}{2} + V(r) + \frac{m}{2} + E_c - E$$ Making \(\frac{E^{2}}{2m}\) subject of the formula, we have: $$\frac{E^{2}}{2m} = E_c - E_c + \frac{m}{2} - \frac{m}{2} - V(r) + E$$ $$\frac{E^{2}}{2m} = E - V(r)$$ .........(5) Equ (5

Any vibration that disturbs air molecule, is capable of making sound. The source of vibration pushes and pull air molecules, causing acoustic signals known as sounds. The sound heard are based on three major factors; that is: The source of vibration that forms the sound waves. The medium which is known as the wave carrier. The receiver that detect the sound. The source of vibration occilates and brings surrounding air into motion through a medium (such as air) and if the receiver is present the sound can be perceived. Sound is a mechanical disturbance that travels through an elastic or viscous medium at a speed depending on the characteristics or features of the medium. While air tubulates, the mass and momentum of the sound are the "sound generators". The diagram below shows how the sound are generated. Diagram showing how sounds are generated.

Sound wave propagation is a wave process. The acoustic signals requires a mechanical elastic medium for propagation and cannot travel through a vacuum unlike, electromagnetic light waves. Sounds travels more quickly in solids, followed by liquid than through gases. The velocity of sound, in a wave form is 331.29 {ms}^-1 through dry air at {0}^oC Sound wave concept When vibration disturbs particle in a medium, then the particle displaces other surrounding particles in that medium. A wave pattern is then formed, when the particle moves in the outward direction continuously. The wave carries the sound energy through the medium from the source and become less intense. The sound energy solely depends on the volume of the volume of the sound; the higher the sound energy the louder the volume. There are three concept of sound wave that causes a sound to be produced. They include: frequency (f), wavelength  \lambda and amplitude (A). The sound wave vibrates at different frequency as

Maxwell equations are a set of four complicated equations that the world of electromagnetism. These equations shows how magnetic fields interacts and propagates. The Maxwell equation have rules, the universe use to govern the behavior of electric or magnetic field. The Maxwell equation was proposed by James Clerk Maxwell (1831-1879). The Maxwell equations are in both differential and integral forms.  Differential form: 1. $$\nabla.D = \rho V$$ 2. $$\nabla.B = 0$$ 3. $$\nabla X E = - \frac{dB}{dt}$$ 4. $$\nabla X  H = \frac{dD}{dt} + J$$ Integral form: 1. $$\int(D.ds) = \int_{v} \rho dV$$ 2. $$\psi_m = \int B.ds = 0$$ 3. $$\int E.dL = -\int_{s} \frac{dB.ds}{dt}$$ 4.$$\int H.dL = \int (J + \frac{dD}{dt}).ds$$ To find out about the derivation of Maxwell equations, click the links below: Maxwell first equation Maxwell second equation   Maxwell third equation Maxwell fourth equation 

The Maxwell fourth equation is called "the modified Ampere's circuital law". Statement: It states that the line integral of the magnetic field H around any closed part or circuit is equal to the current enclosed by the path. Differential form (without modification): That is, $$\int H.dL = I$$ Let the current be distributed through the current with current density J, then: $$I = \int J. ds$$ This implies that: $$\int H.dL = \int J.ds$$ .........(9) Applying Stokes theorem to the LHS of equ(9) to change line integral to surface integral we have: $$\int_{s} (\nabla X H).ds = \int_{s} J.ds$$ Since, two surface integrals are equal only if their integrands are equal. Thus, $$\nabla X H =J$$ .........(10) Equ(10) is the differential form of Maxwell fourth equation (without modification) Take divergence of equ(10) $$\nabla.(\nabla X H) = \nabla.J$$ Since, the divergence of the curl of a vector is zero.  Therefore, $$\nabla.(\nabla X H) = 0$$ It means that $