![\"\"](\"https:\/\/blog.metu.edu.tr\/caglart\/files\/2024\/11\/tab1.png\")
<\/a><\/p>\n\u015eu an tart\u0131\u015fmaya ba\u015flad\u0131\u011f\u0131m\u0131z konuya ait \u00f6nceki DALGA MEKAN\u0130\u011e\u0130 \u2013 a \u2013 ve \u2013 b \u2013 ba\u015fl\u0131kl\u0131 yaz\u0131larda g\u00f6rd\u00fck ki, (Ni\u00e7in \u00fc\u00e7, d\u00f6rt veya daha fazla de\u011fil? Bilinmez!) topu topu iki enerji t\u00fcr\u00fcm\u00fcz var; (\u00e2dete uyup V ile temsil edece\u011fimiz) potansiyel enerji ve (yine \u00e2dete uyup ama bu kez K ile temsil edece\u011fimiz) kinetik enerji. K\u2019n\u0131n her daim \u00bd mv\u00b2 oldu\u011funu biliyoruz ama (potansiyel enerji) V\u2019yi hesaplayabilmek i\u00e7in her \u015feyden \u00f6nce kuvvet ile par\u00e7ac\u0131\u011f\u0131n devinim esnas\u0131nda izledi\u011fi yolu bilmek ve hesaba katabilmek gerekiyor ki, bu hesab\u0131n alt\u0131ndan kalkabilmek her zaman kolay olmuyor. Ama \u015fu kadar\u0131n\u0131 not d\u00fc\u015fm\u00fc\u015f olal\u0131m; V\u2019nin de\u011feri par\u00e7ac\u0131\u011f\u0131n izledi\u011fi yoldan (y\u00f6r\u00fcnge) ba\u011f\u0131ms\u0131z ise bu potansiyel enerji i\u00e7in \u2018korunumlu\u2019 (\u2018conservative\u2019) deyimini kullan\u0131yoruz. \u00d6rne\u011fin yer\u00e7ekimi korunumludur.
\nAra sonu\u00e7 olarak, toplam enerjiyi E ile temsil edersem,
\nK + V = E >>> E\u015fitlik 1
\ndiye yazabilirim.
\nB\u00f6ylelikle de fizi\u011fe biraz ara verebiliriz.
\nS\u0131rada bir \u00f6yk\u00fc var. Sonras\u0131nda, ilk mektep matemati\u011fi daha do\u011frusu aritmeti\u011fi gelecek; \u00fc\u00e7 harfli e\u015fitliklerle ilgilenece\u011fiz. Zira, iki harfli e\u015fitlikler sadece tan\u0131md\u0131r. (*)
\nDaha sonra yine d\u00f6nece\u011fiz fizi\u011fe daha a\u00e7\u0131k\u00e7as\u0131 Dalga Mekani\u011fi\u2019ne. Hem de Richard Feynman\u2019a ait oldu\u011fu iddia edilen \u015fu s\u00f6z hilaf\u0131na: \u201cHi\u00e7 kimsenin kuantum mekani\u011fini anlamad\u0131\u011f\u0131n\u0131 rahatl\u0131kla s\u00f6yleyebilirim san\u0131r\u0131m.\u201d (**)
\nEfendim, rivayet edilir ki, Erwin Rudolf Josef Alexander Schr\u00f6dinger, babayla beraber Alplerde tatil yaparken bir kaza ge\u00e7irir ve k\u0131r\u0131k baca\u011f\u0131 al\u00e7\u0131lan\u0131p ask\u0131ya al\u0131n\u0131r. Patellas\u0131n\u0131 k\u0131rm\u0131\u015f bir \u015fah\u0131s olarak pek iyice bilirim al\u00e7\u0131l\u0131 baca\u011f\u0131n ne demek oldu\u011funu. Zaman ge\u00e7mek bilmez bir t\u00fcrl\u00fc.
\nNeyse ki, bir ahbab\u0131 duman\u0131 \u00fcst\u00fcnde bir matematik kitab\u0131 getirir ziyaretinde, Schr\u00f6dinger can s\u0131k\u0131nt\u0131s\u0131n\u0131 bast\u0131r\u0131r diye umarak.<\/p>\n
Dikkate \u015fayand\u0131r; de Broglie\u2019in dalga-par\u00e7ac\u0131k ikili\u011fi kuram\u0131n\u0131 1924\u2019\u00fcn sadece bir iki y\u0131l sonras\u0131n\u0131 g\u00f6stermektedir takvimler ve kader mi dersiniz, nasip mi; yazarlar\u0131 Courant veya Hilbert de\u011fil de, can s\u0131k\u0131nt\u0131s\u0131ndan muzdarip okuyucusu Schr\u00f6dinger g\u00f6r\u00fcr kitaptaki hazineyi!? O hazine de, konum ve zaman i\u00e7eren baz\u0131 diferansiyel denklemlerin \u00e7\u00f6z\u00fcm\u00fcd\u00fcr.<\/p>\n Kolayl\u0131k olsun diye, x-koordinat\u0131 ve t-zaman\u0131 i\u00e7eren bir fonksiyonu f(x,t) bi\u00e7iminde, yahut daha \u00e7ekici g\u00f6r\u00fcns\u00fcn diye \u03a8(x,t) bi\u00e7iminde ifade edelim. Schr\u00f6dinger\u2019in ilgisini yo\u011funlukla \u00e7eken diferansiyel denklem,\u00a0 C<\/em> herhangi bir ger\u00e7ek veya karma\u015f\u0131k (\u2018complex\u2019) ama sabit bir say\u0131 olmak \u00fczere \u015fu idi;<\/p>\n Bak\u0131\u015flar bu denkleme kilitli iken yak\u0131n ge\u00e7mi\u015fi \u015f\u00f6yle bir taramak m\u00fcmk\u00fcn: Planck foton enerjisinin paket\u00e7ikli (\u2018quantised\u2019) ve hf de\u011ferinde oldu\u011funu, Einstein dalgaboyu \u03bb olan fotonun do\u011frusal momentumunun h\/\u03bb oldu\u011funu, de Brogliie de do\u011frusal momentumu p olan bir taneci\u011fin dalgaboyunun h\/p oldu\u011funu bulmu\u015ftu. B\u00f6ylelikle, madde_dalga ikili\u011fi fikri hayli yayg\u0131nca kabul g\u00f6r\u00fcr olmu\u015ftu ve ama madde dalgalar\u0131n\u0131n \u015fekli \u015femali halen muamma idi. Daha da \u00f6nemlisi, taneciklerin devinirken izledikleri yol yani y\u00f6r\u00fcngeleri gayet kesinlikli olarak belirlenebiliyordu Klasik Mekanik dilinde. Acaba, ayn\u0131 par\u00e7ac\u0131klar\u0131n devinimlerini betimleyebilmek i\u00e7in dalga \u00f6zelliklerinden de yararlan\u0131labilir miydi? Evet ise, nas\u0131l? Bu son denklem uzun y\u0131llar sadece sanal bir sonsuz derin potansiyel enerji kuyusu i\u00e7indeki par\u00e7ac\u0131k, ger\u00e7ek\u00e7i harmonik sal\u0131nga\u00e7lar (\u2018harmonic oscillator\u2019) ve Hidrojen atomu (bir proton bir elektron) problemini \u00e7\u00f6zmekte kullan\u0131labildi. Sevgili Oktay Sinano\u011flu hocan\u0131n makine dilini (\u2018assembler language\u2019, \u2018assembler code\u2019) yard\u0131m\u0131yla birka\u00e7 oda kaplayan bilgisayarda \u00e7ok elektronlu atom \u00e7\u00f6z\u00fcmlerinde n\u00fcmerik sonu\u00e7lar elde etmesiyle cin \u015fi\u015feden \u00e7\u0131k\u0131p her yan\u0131m\u0131z\u0131 \u00e7epe\u00e7evre ku\u015fatt\u0131.<\/p>\n (*) Emilio Segre\u2019nin \u201cX-I\u015f\u0131nlar\u0131ndan Kuarklara\u201d kitab\u0131n\u0131 g\u00fczel T\u00fcrk\u00e7emize \u00e7evirirken, Segre\u2019den \u00f6\u011frenmi\u015ftim; Fizi\u011fin en kapsay\u0131c\u0131 denklemleri en yal\u0131n, yani \u00fc\u00e7 harfli olanlard\u0131r; F=ma, E=mc\u00b2 gibi\u2026 Fizik \u20139 \/ c\u2013 \u0130\u00e7erik: Aslanlar\u0131n, kaplanlar\u0131n, sizin ve benim ile ta\u015flar\u0131n, atomlar\u0131n, elektronlar\u0131n ve atom alt\u0131 veya \u00fcst\u00fc t\u00fcm par\u00e7ac\u0131klar\u0131n, ez c\u00fcmle hepimizin dalgalar\u0131ndan s\u00f6z ediyoruz. Nam\u2019\u0131 di\u011fer; ond\u00fcleli mekanik! \u015eu an tart\u0131\u015fmaya ba\u015flad\u0131\u011f\u0131m\u0131z konuya ait \u00f6nceki DALGA MEKAN\u0130\u011e\u0130 \u2013 a \u2013 ve \u2013 b \u2013 ba\u015fl\u0131kl\u0131 yaz\u0131larda g\u00f6rd\u00fck ki, (Ni\u00e7in \u00fc\u00e7, d\u00f6rt veya […]<\/p>\n","protected":false},"author":1425,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[1],"tags":[],"class_list":["post-303","post","type-post","status-publish","format-standard","hentry","category-genel"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/303","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/users\/1425"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/comments?post=303"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/303\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/media?parent=303"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/categories?post=303"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/tags?post=303"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}<\/a>
\nOkuyucular\u0131m\u0131z, bir ihtimal, Courant ile hen\u00fcz tan\u0131\u015f\u0131yordur ama David Hilbert gediklilerimizdendir.
\n<\/a><\/p>\n<\/a><\/p>\n
\nNOT: Hemen alttaki matematiksel analizle u\u011fra\u015fmak istemeyen okuyucu, yaz\u0131n\u0131n sonlar\u0131ndaki \u00d6ZET\u2019e (ye\u015fil renkli zemin) ge\u00e7ebilir.<\/p>\n<\/a>
\n<\/a><\/p>\n
\n(**) Bu s\u00f6ze, \u015fu adreste rastlad\u0131\u011f\u0131mda \u015fa\u015f\u0131rd\u0131m: https:\/\/mathshistory-st–andrews-ac-uk.translate.goog\/Biographies\/Feynman\/quotations\/?_x_tr_sl=en&_x_tr_tl=tr&_x_tr_hl=tr&_x_tr_pto=tc \u015e\u00f6yle yaz\u0131yordu o sitede: \u201cI think that I can safely say that nobody understands quantum mechanics. The character of physical law<\/em> (Cambridge, USA, 1967)\u201d \u015ea\u015f\u0131rd\u0131m \u00e7\u00fcnk\u00fc kaynak olarak g\u00f6sterilen kitab\u0131 erken(!) gen\u00e7lik zamanlar\u0131mda okumu\u015ftum ama o s\u00f6z\u00fc an\u0131msayamad\u0131m. \u201cVitamin kullanma zaman\u0131m gelmi\u015f olabilir mi?\u201d diye merakla ve inatla yeniden bakt\u0131m. Yok! Dahas\u0131, an\u0131lan kitapta \u2018quantum mechanics\u2019 s\u00f6zc\u00fckleri bu tamlama halinde on kez, tekil \u2018quantum\u2019 s\u00f6zc\u00fc\u011f\u00fc ise on sekiz kez ge\u00e7iyor.
\nNeyse, i\u015fbu yaz\u0131y\u0131 yay\u0131mlad\u0131ktan sonra behemehal ba\u015flayaca\u011f\u0131m \u201cThe character of physical law\u201d\u0131 yeniden okumaya. Gayet heyecan verici bir ser\u00fcven olaca\u011f\u0131ndan ku\u015fkulanm\u0131yorum.
\n(***) Ger\u00e7i ba\u015fka \u00f6l\u00e7\u00fctler de vard\u0131r; s\u00fcrekli olmak ve s\u0131f\u0131rdan farkl\u0131 ikinci t\u00fcreve sahip olmak gibi. Bu t\u00fcr fonksiyonlara, fiziksel fonksiyon denir.<\/p>\n","protected":false},"excerpt":{"rendered":"