The domain of quantum mechanics

The domain of quantum mechanics


Roughly speaking quantum mechanics is required when the scale of the phenomenon being very small on the order of atomic dimensions (ten raised to the power minus ten metre). We need quantum mechanics to explain the behaviour of electrons in atoms or solids or the behaviour of atoms in molecules. We may use classical mechanics to describe the motion of macroscopic objects such as balls, Wheels, pendulums and projectiles.

An accurate establishment of domain of quantum mechanics is based directly on the Planck’s constant h = 6.626 x ten raised to the power of minus thirty four joule-sec. Planck’s constant has the dimensions of energy times time, a quantity known in classical mechanics as action. The dimensions of action can easily be shown to be the same as momentum times distance or angular momentum. Hence the following conclusion can be arrived regarding the domain of quantum mechanics.

“If the action or angular momentum involved in a given physical even is on the order of Planck’s constant, then we must use quantum mechanics to describe the event accurately. If the action or angular momentum in a physical event is orders of magnitude larger than Planck’s constant, classical mechanics will describe the event with satisfactory accuracy.”

The angular momentum of the earth orbiting around the sun is ten raised to the power one hundred and two times h, of the earth revolving about its axis is ten raised to the power sixty eight times h. The angular momentum of a bicycle wheel about its axis is ten raised to power thirty two times h, of the balance wheel in a watch approximately ten raised to the power twenty four times h. Similarly the action involved in shooting a bullet from a gun is perhaps ten raised to the power thirty five times h and that of accelerating an electron to the screen of a television tube is ten raised to the power ten times h. In all these events the quantization of the action is irrelevant because undetectably small compared with the total action involved. 

Quite by contrast the angular momentum of the electron about the nucleus of an atom is only a few times h as also the angular momentum of rotation of a gaseous molecule. The action involved in the emission of radiation of an atom is generally equal to h or at most to a few times h. For these physical systems and these events the quantization of action and of angular momentum is eminently relevant and we must use quantum mechanics to calculate the properties of such systems and their interaction with applied forces.

Classical mechanics is completely definite theory in the sense that the computational procedures do not introduce any statistical uncertainties into the system themselves. 

Quantum mechanics on the other hand is fundamentally a probabilistic theory.

The king of pop Michael Jackson

Michael Jackson

The King of Pop Michael Jackson has died after suffering a fatal heart attack at the age of 50. The Thriller legend was taken to hospital earlier today after frantic aides found him unconscious at his mansion in Holmby Hills, Los Angeles. 

According to TMZ.com, medics administered CPR en-route to L.A.'s Cedars-Sinai hospital to try and keep him alive, but he was totally unresponsive. 

After just a few hours in a coma, Jackson died as his family members, including his mother and brothers, rushed to be at his bedside. 

The seventh child of the Jackson clan, the singer shot to fame as part of The Jackson 5 at the age of 11, alongside his brothers Jackie, Tito, Jermaine and Marlon. 

Due to his stunning vocals and dancing ability, Jackson became the stand-out star of the family group, and launched his solo career in 1972 with the release of Got to Be There. 

Interest in the star grew to phenomenal proportions as he released his iconic Thriller LP ten years later. The disc went on to become the biggest selling record of all time - shifting a staggering 109 million copies to date. 

He quickly became the forthright pop musician of the 1980s, and garnered a cult-like following due to the popularity of his music videos and iconic dance moves, including the Moonwalk. 

Picking up 13 Grammy awards throughout his career, as well as 13 number one singles in the U.S., Jackson achieved a number of entries in the Guinness World Records - including the accolade Most Successful Entertainer of All Time. He released ten best-selling albums. 

But the superstar's career hasn't been without controversy, starting with the drastic change in his appearance, most notably the colour of his skin, which some assumed the star had bleached white. Jackson refuted the rumours, insisting he suffered from pigmentation condition vitiligo. 

Often thought of as child-like himself, especially after purchasing sprawling California estate Neverland and decking it out with funfair rides and his own private zoo, the world was stunned as a 13-year-old boy and his father accused the singer of child sexual abuse. Jackson, who was strip searched at his ranch, vehemently denied the claims, settling out of court with the child's family for $22 million (GBP14.7 million). 

However, similar accusations reapperaed years later, and in 2003 it was alleged he sexually abused another young boy. His trial began in 2005, with hundreds of fans supporting him daily outside the Santa Maria, California courthouse. After five months he was acquitted on all counts. 

In 1993, at the height of the first child abuse scandal, Jackson married Elvis Presley's daughter Lisa Marie. Presley explained that their relationship sprung out of an understanding of the intense pressures of fame, for which her father had also suffered. The world's media speculated furiously over the intricate details of their relationship, insisting the union was a ploy to shift focus on the sex abuse allegations. The pair later divorced less than two years later. 

As Jackson embarked on his first world tour since the controversies, the HIStory tour, it was announced he had married dermatologist nurse Deborah Jeanne Rowe, who fathered the first of the star's children Michael Joseph Jackson. Jr, who he later dubbed Prince, in 1997. A daughter, Paris Michael Katherine Jackson, was later born. The couple subsequently divorced in 1999, with Rowe giving the star full custody rights of their children. 

The hitmaker kept a low-profile following his HIStory tour, and returned to the public spotlight in 2001 to mark his 30th anniversary in the music industry. He appeared onstage with his brothers for the first time since 1984, and was joined by a string of superstars including Whitney Houston, Usher and Britney Spears who paid homage to the star's stellar career. 

After the release of his relatively poor-selling Invincible album in 2001, Jackson welcomed a third child the following year. Prince Michael Jackson II, known as Blanket, was delivered by an unknown surrogate mother. The singer attracted controversy again after he dangled the tot from the balcony of a Berlin hotel. 

Another spell in the showbiz wilderness followed, until it was announced in February this year that the star would be making a stage comeback for a 50-date residency at London's 02 Arena. 

Jackson was reported to have pulled in $75 million (£50 million) from the dates, to aid his dire financial situation, following the foreclosure of his Neverland Estate to service a loan Jackson owed on the property. Experts feared the star wouldn't be well enough to perform at the shows after reports leaked he was suffering from skin cancer. Only last month, the superstar cancelled the first week of the tour, insisting he needed more time to prepare for the extravaganza. 

Michael Jackson, dead at 50 years old, is survived by his three children, his mother and father; Joseph and Katherine, and his five brothers and three sisters, Janet, Rebbie and Latoya