05 SOLVED PROBLEMS - Nuclear Physics

MONTE CARLO Method

AGE of EARTH

ABSOLUTE MADNESS - Poetry

QUANTUM MECHANICS : An Outline

“You can never verify a theory, you can only verify its predictions!” : V.Balakrishnan

QUANTUM  MECHANICS ::

The behaviour of any classical system takes the system through different states. A ‘state’ is as defined by the value of the various dynamical variables at that particular instant. In physics, essentially we are talking about a number, in a measurement, that quantifies the particular variable.

Quantum mechanics replaces the dynamical variable with a linear operator, with its accompanying rules relevant to that mathematical object  º OPERATOR.

For dynamical variables the value of a measurement would have to be necessarily a real number. The operators that would represent a dynamical variable, hence qualify to be of a different kind   º hermitian operators.

In a classical dynamical system, when we make a series of measurements of the same property[variable] we expect to get a set of different values, that may be decided by the measurement process. To get to an accurate prediction of the actual value we resort to statistical procedures. This takes care of the gross, systematic & random errors of the measurement.

In a QM system, it is conceptualised that the system exists in its various possible allowed states and the act of measurement makes one such state to show up & the particular value appropriate to that state º the ‘eigen’ state is measured as the ‘eigen’ value of the dynamical variable.

The orthodox position : The particle was not really anywhere.

It was the act of measurement that forced the particle to ‘take a stand’.

JORDAN said it plainly, “ Observations not only disturb what is to be measured, but they produce it . . . . We compel (the particle) to assume a definite position.

This view [the so-called COPENHAGEN interpretation] is associated with BOHR and his followers. Among physicists it has always been the most widely accepted position.

QM gives us a mathematical procediure to calculate the expected [most probable] value for the measurement of a particular dynamical variable, given its complete set of eigenstates. There is an integral definition for the expectation value.

So, in QM we come across a new concept for a QM system. The uncertainity in the estimation of the canonically conjugate variables(the state)is not an artefact of the measurement process, but an inherent characteristic of the system itself, which is described by the Schroedinger’s equation !

This was Heisenberg’s valuable contribution to an understanding of QM.

Let it be said that QM is not completely put as set in this brief outline. This is just an indicator and would definitely look very intriguing for the uninitiated! Also, QM itself is deemed to be quite not so complete! What could be said with a certainity is that it does explain very many phenomena, especially at microscopic scales and has given all the magic that Physics has done for this civilisation, with modern technology!

EPILOGUE -

 “Anyone who is not shocked by quantum theory has not understood it.”

                                                                                  -- -- -- NIELS BOHR::

.           .           .z

The Textbooks :

1.   A TEXTBOOK OF QUANTUM MECHANICS, P.M.Mathews & K.Venkatesan,

2^nd edn.(2010) TMH, India.

2.   QUANTUM MECHANICS, V.Murugan (2014) Pearson, India.

3.   Listen to one of the best Physics teachers on this planet :

http://freevideolectures.com/Course/2669/Quantum- Physics

 V. Balakrishnan on Quantum mechanics!

March 2017                                             qed n_ln

Ode to GOOGLE!

On this special day i request to be excused for a posting in my native tongue -
My ode to GOOGLE SEARCH on this particular day:
–----------------------------
கண்ணிமைக்குந் தருணத்தில், மின் அசைத்துப் போனாய்.
உள்ளூரப் பாய்ந்தாற்போல மெய் சிலிர்க்க வைத்தாய்!
கற்பக விருட்சமாய் இங்கு வந்தாய்,
கேட்டபின்  நீயே தந்தாய்!
யோசிக்கும் முன்பே, நேசிக்க வைத்த
இணையதளம் உனக்கிருக்க,
காலம் காலமாய் தொடரும் தேடலின்
வேட்கைத் துணையாய்
அமர்ந்தப்பின், என்னுடனே, எங்கும்
எப்போதும் கூடியிருந்தாய்!

வாழ்வு ஒரு தேடல் என்பார்!
"கூகுள்" ஒரு தேடல் என்பார்!
___________________________●✍️நலநா

DEDICATED to :GOOGLE SEARCH ,
the game changer in education, knowledge seeking & awareness ,of the past decades.

FOOD FOR THE COMPUTER

-----------------------------------------------------------

  

PAIR CREATION & ANNIHILATION - Nuclear Physics

PAIR CREATION & ANNIHILATION

        Relativity and the mass-energy relation,

E = mc²                  . . .(1)

 that came from it has been used to explain some natural phenomena that occur in high energy physics. Observations are made of elementary particle-antiparticle pairs that get created or annihilated.

          Conversion of mass to energy, as taking place with various processes like burning fuels, fission or fusion are low yield processes and not all of the available energy can be converted. Matter – antimatter reactions are the exceptions to such processes.

          In pair production, electron-positron, for instance, a photon transforms to material particles. In any such process, energy, momentum and charge must all be conserved. The minimum energy required for the production of the positron-electron pair would be

2 m_e c² = 1.02 MeV            . . .(2)

where m_e is the rst mass of the electron/positron.

          As a photon’s energy is given by ‘hf’, the minimum energy requirement for the above process(2), would decide the photon’s frequency,

hf_min = 1.02 MeV                . . .(3)

Pair production does not occur in vacuum and takes place only in the presence of a massive particle[like atomic nuclei] to enable simultaneous conservation of energy & momentum.

PAIR ANNIHILATION

            Pair annihilation is the inverse of pair production. An electron & positron, initially at rest, combine and then disappear to create two photons. Two photons are needed as the initial momentum of the source pair is zero. Momentum can be conserved only if two photons of same energy and momentum[magnitude] move of in opposite directions!

--        --        --        --        z

March 2017                                                                                        qed n_ln

STATEMENT OF PURPOSE : "YES!" : An OUTREACH.

Good Morning INDIA!

The main setting for this tool is to enable the search for clarity of the unexplained.
A training as it may be for the young.
This is mainly directed towards school going children anywhere in the world and for the entry undergrads.

Any interested person could post their queries, unsolved problems or honest doubts.
A solution shall be attempted within the framework of the knowledge, ability and personally allowable alacrity of I.

I again salute GOOGLE for their game changer of the past decades - GOOGLE SEARCH ENGINE, which has benefited awareness & knowledge seekers!

Please do send your postings to my email : reachnln@gmail.com

The answers will be posted with reference at my earliest possibility!
I am a one man function at the present time.:-)

THANK YOU!

CHENNAI, those were the days! : FICTION

Those were the days, when my grandparents had to go to the Library to check out some detail. A letter to their son in Great Britain meant a lot of things. . .  letter to be written, enclosed in cover, taken to the Post office, correct stamp charge to be found after weighing, stick the purchased stamps and post it. Then, wait for a week to assume that the letter had reached their son in GB. Everything took time and some effort. Nowadays, the same things take just a few minutes, only the medium has changed.

As I think of all these things and look ahead to some not so very far day I see some fantastic things. . . . . . . .  . .

·Wake-up call on the networked system in my house is in my mother’s voice. Only occasionally I choose the option of setting some other voice. ·The bathtub I get into, sets the water temperature to match my body temperature and the ambience. After a comfortable bath, breakfast follows.

· As I take my breakfast my cellular phone rings and to my surprise it is my Uncle and Aunt speaking from MARS. They had decided to take a vacation there. On the video phone, I see that they are so happy as they talk to me. Nice thing. I should ask my daddy to take us there for the next holidays.

· Breakfast over and I wait for my pick-up vehicle. I lived in the NEW city.

·The entire community is mapped onto a three dimensional mobility structure. Time optimised pathways for that particular day take me to my workplace in the shortest time. All this is something like the suburban railway system in the OLD city, but more intelligent here.

In INDIA, the OLD continued with the NEW.

We are now the leaders of the WORLD and only CHINA had peer status in some WORLD & Planetary Organisations.

          At the workplace, the Entrance chamber had the Identification pad on which one had to stand. The body structure of every staff member is scanned simultaneously with an eye check and EEG scan. When everything checked out, the entrance door would open, to let one in.

If some harmful restlessness in the brain activity is detected the display would indicate this to the person and also advise leave if the abnormality was above the prescribed level.

After work time got over I return home. Once there, I find that my brother has had some accident and twisted his knee joint. Immediate reference to our Doctor and he conducts a networked check on my brother’s blood through a sample drop that my brother had dropped into the Analysis vial at the home node. After the Doctor’s System goes through the analysis the particular chemical to prevent any infection is prescribed for my brother.

BIOINFORMATICS had made medical treatment so very accurate and personalized. Also operations had become more so precise with the MEMS [Micro-Electro-Mechanical Systems] technology. The design for these devices was mostly being done in INDIA, the Hardware was being made in CHINA, while even there a few basic things were being manufactured in INDIA. Both INDIA and CHINA had some of their less crucial centres located in the USA, Russia and a little bit in GB. This helped the World economy.

If one needed to relax, one took time of to visit one’s house in the OLD city and went around in one’s HYDROGEN driven cars.

AIR-Travel had become so very fast with advances in technology. Safe Speeds had increased to nearly four times or more of the present standard.

I could go on and on about ALL the advances.

So much; so much would have changed.

My father and mother may feel happier to be left alone in our OLD city home – with their fast [5GHz] handhelds which had everything and the Planetary TV Broadcast for their entertainment. Their occasional picnic was a run in their HYDROGEN driven cars to some nice countryside! 

[From n ln , in JOURNALISM ONLINE, Issue No: 69, NEWSLETTER, November 2005
http://groups.yahoo.com/group/journalismonline/message/69

[ED.: N. Watson Solomon (aka Nirmaldasan)]

--        --        --        --        -- z?

March 2017                                                                                qed_n ln

04 SOLVED PROBLEMS - Nuclear Physics

03 SOLVED PROBLEMS - Free Body Diagrams

Simple EMIL Train Video

Simple Train from 'You Tube"

Simple EMIL Train

* Bare COPPER wire & magnets for experiment

02 SOLVED PROBLEMS - Aerosols

01 SOLVED PROBLEM - Dynamics

ALTERNATING CURRENT POWER TRANSMISSION

SOUND of SILENCE

FRICTION

The Anterior

It is an eternal search.

In the microcosm of one such dimension, during the game of searching; as we discover , we start seeing that there is an infinity left to know.

In that personal path of discovery, there are a numerably large number of narrations, solved problems and things to know about. All this will be shared for all to know.

With the utmost of sincerity i place on record that whatever has been achieved or compiled was made possible by my teachers(my father was one of them) & the greatest enabler called the GOOGLE SEARCH ENGINE which gets me information from that humungous library -the WWW. The illustrations in my postings are done with the help from ADOBE ILLUSTRATOR & elements from GOOGLE IMAGES.

Thank you  நன்றிகள்!

Laksh.