Apa itu Nombor Kuantum?

Nombor kuantum boleh dikategorikan sebagai salah satu topik yang penting dalam mempelajari subjek mekanik kuantum atau umumnya teori kuantum. Namun hingga kini, ramai yang masih keliru atau masih menginginkan penjelasan menyeluruh berkenaan nombor kuantum ini. Maka, inisiatif ini diambil bertujuan untuk memberikan gambaran malah pemahaman padu berkenaan nombor kuantum. Beberapa istilah yang digunakan adalah istilah biasa yang telah pun diperkenalkan dalam subjek mekanik kuantum (adalah lebih berkesan jika pembaca telah pun memahami istilah-istilah tersebut).

Istilah nombor kuantum muncul apabila ingin mencari penyelesaian kepada persamaan Schrodinger. Persamaan Schrodinger ini adalah persamaan gelombang dalam fungsi gelombang untuk mencirikan sesuatu zarah pada sesuatu titik dalam satu-satu masa. Adalah diketahui umum, mekanik kuantum mementingkan ruang kompleks sebagai sistem kerja berbanding mekanik klasik yang lebih kepada ruang nyata. Dan persamaan Schrodinger yang diperkenalkan oleh Erwin Schrodinger (ahli fizik terkenal) dilihat sebagai satu-satunya persamaan paling berkesan untuk mencirikan sesuatu zarah dalam ruang kompleks itu. Dengan berpandukan kepada sesuatu situasi kompleks berkenaan terdapat beberapa nombor kuantum yang boleh dikira. Sebagai contoh, dalam ujikani osilator harmonik (ujikaji satu dimensi zarah yang dipengaruhi oleh keupayaan V=[1/2]kx²), nombor kuantum yang terlibat adalah n, yang mana n ini mewakili paras tenaga (energy level) kepada osilator harmonik.

Satu lagi contoh adalah dalam tiga dimensi untuk satu elektron bagi atom, nombor kuantum yang terlibat adalah n, l dan ml. Ketiga-tiganya mewakili paras tenaga (energy level), momentum sudut (angular momentum) dan momen sudut (angular momen) kesemuanya pada arah paksi z. Terdapat satu lagi nombor kuantum iaitu ms yang mewakili spin elektron.

Jika berpandukan contoh-contoh diatas, dapat diperhatikan bahawa nombor kuantum adalah sesuatu yang diskrit (denumerable) atau sesuatu yang boleh dikira. Hanya perlu meluaskan lagi situasi kompleks (sistem kerja kompleks) sedia ada, maka kita akan dapat mencari atau mengklasifikasikan nombor-nombor kuantum yang mewakili perwakilan-perwakilan tertentu. Dan ini memang sesuatu yang boleh berlaku.

Nota: kesemua ujikaji merupakan masalah penyelesaian kepada
persamaan Shcrodinger

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File translated from T_EX by T_TH, version 3.74.
On 30 Aug 2006, 10:32.

Theoretical Sciences League

It’s now a fact that no more TSL (Theoretical Studies Laboratory). It’s been officially announced by the senate that our lab will be exiled from our previous place and now we recite under the physics department. Still we keep on maintaining the plan for having the next TSL ELS V (namely Theoretical Studies Laboratory, Expository Lecture Series) due on the 12^th – 15^th December 2006 carries the theme “Computational Physical Sciences 2006”. Formerly our ELS I, II, III and IV has successfully create positive response from local researchers especially the theorist. So it’s really a good thing to have the lecture series being continued. Then today we resume our 3^rd meeting of the committee. And funny thing that we’ve come up with a new name of TSL where everyone kind of agree with it. So instead of Theoretical Studies Laboratory we agreed on Theoretical Sciences League (reminds me of the cartoon Justice League). For me it’s a very cool name. Well, it suppose to be that way. Better hope that it will bring more joyous and prosperous to the group.

Reign by the Azzurris

The World Cup 2006, Germany has now ended (Olympiastadion - Berlin). And the winner, as I’m dying want it to be was ITALY…, which make France fulfilling the second title. Not once, ever imagine that the Azzurri can actually be the 2006 winner. This is their 4^th winning for the World Cup after few years back with a ‘heartbreaking’ journey. Believe it or not the fact that with all their previous defeated was now prevail with a big of a winning celebration. It’s really remarkable. And thank must goes to the ‘only’ David Trezeguet (the one who crash out Italy dream in the EURO 2000 with his golden ball) for not to be able handling his penalty accordingly. Where as for the Italy, they completed the 5 penalties elegantly…

I must say that during the match, the two of us was kind of hoping that both of our team could make it in claiming the winner title. I was totally nervous about Italy becoming the winner, since France can actually creating bizarre and dangerous attacks while they in the field. Not to mention that they did have a tiptop well-known player in every position, Henry (forward), Zidane (midfield), Thuram (defend) and last man Barthez (keeper). This not happen among the Italians. Very few of them are recognizable, while the others were just an ordinary player. Still, last night game was fantastic (sorry that I was actually ‘on’ and ‘off’ while watching), but the game was really full of a drama. The top story would be, Zidane's shocking red card penalties in his 108 caps of international appearance. Instead of ending his international carrier gracefully, he just have to accept the fact that it’s the other way around. Another was, the game itself. France did actually have beautiful chances to ‘break’ Italy’s net, but all of their ‘trying’ being denied by the Italians whole-heartedly. Buffon (Italy’s keeper) performed well, Henry was somehow outshine (as always), Cannavaro in his full action as an outstanding captain, their passing are excellent, their crosses are nice, some with injury problems (poor Viera), some get too rough and other hectic wild actions…I was really enjoy. I think everyone does.

Finale, we just have to put a stop since a month has ended for the soccer fan now. No staying up late for football and no mamak stall during the night (for the game). Everyone will afterwards resume with his/her normal life. Thank you for the previous month for essentially creates a healthy environment with one game, one nation, one excitement and one celebration through out the whole world. All in one…

Victory for Italy, Doom for Germany

The semi-final match between Italy-Germany in the World Cup 2006 was indeed a fascinating match to watch. Even more interesting, Italy won the game (they’ll facing either Portugal or France in final). After sleeping for about an hour or so, I woke up at around 3am to watch the live match from Westfalenstadion, Dortmund. Truly I must say that, chances for Italy was quite small if to compare to Germany (the home ground team) who get full supports from their fans. But still I just have faith for Italy. I love Azzurri since long time ago, when I first watch them played during the EURO 2000 (they lost to France in semi-final). How sad…during that time, David Trezeguet scored the golden goal for France which spoiled Italy’s dream to win the EURO. I remembered the looks on Francesco Toldo (a very talented keeper) plus other Italy player too while ‘taking’ their lost. Really I am. During that time also, I considered France has a better ‘luck’ than Italy. While, in the World Cup of 2002, again no luck for the Azzurri (been defeated to the South Korea in the penalty shoot-out plus not really outshine during the EURO 2004 either). Well, it’s a game by the way. The answer is just between two, either one be defeated or one with victory. That’s for sure. Still, as a devoted fan, I can feel the pain too.

So back to Germany 2006, most of the World Cup fan predicted that Germany would go to the final facing another giant team, Brazil (oopss…Brazil lost to France in quarter). But sadly to say, the prediction went wrong. I mean totally (sorry my dear). What can I say about it? But last night match, both team perform a highly skillful football. Of coz, Italy played very well last night. Instead of just keeping on defend; they actually give a counter-attack through out the game. I just can’t believe myself. And it did give Germany a pressure. Both team played consistently that make them both tight nil to nil and drag them to the extra time. I was so amazed and somehow worried about that game, where as usual I just hope for the penalty shoot-out. To me, play for the shoot-out will definitely a fair game. And I don’t mind if Italy lost in the penalty shoot-out but not with a goal. It should be tight. Suddenly, miracle happen, on the 119 minutes, Grosso, Italy defender, with his left-foot kick the ball passing Lehmann (Germany keeper) that make the Azzurri with one goal a head. What a nice goal. And it’s not just stop there, because a minute later, Del Piero (sharing a one-two passing) found a chance to put the ball again into the German’s net. Arrghh…I think Klinsmann will just have to accept the fact that their journey towards the world cup’s winner ends here. Still, two thumbs up for Germany for making the game challenging and interesting. It’s just that no luck for them this year.

P/s- Actually, there’s something about Italy. For me is about how they play. Always convenient with 4-4-2 structure, they defend more than attack. That’s why, if one noticed how Italy win the games with a very small number of goals. They aimed averagely…

A Big of A Thank

I just have to put an “emergency” stop button (postponing) of my intention to upload academic stuffs. I just haven’t had the slightest idea on where or what to start. Since right now, I’m working with quite technical stuffs (which demanding a great deal of mathematical understanding). So to think of posting up those idea, was a un-suit things to do.

Plus, I am sadly to say that, starting next week, there will be no TSL. Yes, my precious lab will be shutting down which left us only the member of the lab. No TSL (Theoretical Studies Laboratory) anymore and afterwards no TSL announcement jamming everybody emails. Huh!…how sad. I’ve been with this lab since 2003, and what can I say was; I have gain lots from it. My career, my knowledge, friends (a really nice friends), new experience, techniques, new stuffs, new interest, the not the good ones, the sad ones, the funny ones, and believe it or not even my love ones. How sweet…

So, today (as our last day) I would like to take this opportunity as to give a big appreciation to the TSL as being the best platform so far providing me with lot lots of valuable stuffs. I must say, I’ve started a ‘real’ journey of life with the TSL. I won’t forget the happiest things we’ve shared together and with this, I will miss ‘you’. We all do…

Positive Desire

I found an interesting idea on what kind of materials do I need to include in this upcoming totally new blog. I feel it would be interesting if in some sort I can actually provide a basic simple introduction (rudimentary level) or simple understanding on few topics related to theoretical physics. Those are very wide to be discussed out, so I might choose to explain (try) related topics on quantum mechanics and some purely mathematical tools or properties. I was really inspired by my sifu to try to develop a positive platform for spreading knowledge especially the understanding of quantum mechanics.

In my former "Me, Myself and ???", I’ve written few on what I do for research, some basic knowledge on wave function, why quantum, properties of quantum mechanics, Hilbert space, very least on purely mathematics properties (very much related to my research) and also other proximity statement of theoretical understanding. The rest was just a bunch of a lame writing about myself.

So right now I am trying to collect and think of some good materials plus critical mass topics to be highlighted (especially to quantum studies) that can provide a profound inputs to those who might be interested in this area.

Way to go…

Welcome

For some reason (funny one), I've just decided to make another blog for myself.

Check it out!

p/s-previous posted was in the "Me, Myself and ???" entry