Ana sayfa Algoritma Özdeğer ve Özvektörlerin Python Programlama ile çözümü

Özdeğer ve Özvektörlerin Python Programlama ile çözümü

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Özdeğer Denklemi

Özdeğer ve Özvektörlerin Python Programlama ile çözümü

Kuantum mekaniği içinde garipliklerin  olduğu bir mekaniktir. Biraz matematiksel yönü ağır bir alandır. Kendine has ve sadece kuantum mekaniğinde geçerli olan kavramlar bulunmaktadır. Bunların başında süperpozisyon, dolanıklık, teleportasyon, belirsizlik gibi kavramlar gelmektedir. Kuantum mekaniğinin varsayımların başında dalga fonksiyonu vardır. Bu dalga fonksiyonu mekaniksel sistemin tüm bilgilerini içermektedir.  gibi fonksiyon var. Sistemin her şeyini biliyor. Zaman ve koordinatlara bağlıdır. Hem reel hemde komplex olabilir. Hilbert uzayının tüm özelliklerini sağlıyor. Hilbert uzayı çok uzun bir konudur. Bu alanda çalışanlar hilbert uzayını iyice kavramalıdır. Öz olarak söylersek  Hilbert uzayı bir iç çarpım uzayıdır. Bu uzayın en temel özellikleri tek değerlidir. Sonlu olmalıdır. Sürekli olmalıdır. Kendisi ile skaler çarpımının yapılabilmesi gerekir. Dalga fonksiyonu tüm bu özellikleri sağlamalıdır. dalga fonksiyonun  karesi taneciğin uzayda herhangi bir noktada bulunma olasılığını verir. Hilbert uzayının diğer bir önemli özelliği ise elemanlarını birbirine dönüştüren komutlara operatör (İşlemci) denir. Bu müthiş bir olaydır.  Bir operatör dalga fonksiyonuna uygulandığı zaman sistemin gözlenebilen bir özelliğini vermektedir.

Schrödinger denklemi kuantum mekaniğinin en önemli denklemlerinden biridir.   Bu denklem bir özdeğer denklemidir.  Kuantum mekaniği bir özdeğer denklemidir şeklinde bir yargıya varabiliriz. Kuantum bilgisayarların matematik modellemesi özdeğer denklemidir. Kuantum mekaniğinde bu kadar önemli özdeğerler matematiksel olarak tanımı çok basittir. Özdeğer kavramını açıklamak için öncelikle özvektör kavramını açıklamak gerek. Bazı vektörler bir A matrisi ile işleme girdikleri zaman yön değiştirir, bazıları ise değiştirmezler. Bazı özel x vektörleri, Ax vektörü ile aynı yönde kalmaktadır. İşte bu vektörlere “özvektörler” denir.   olacak şekilde     skalerleri ve sıfırdan    farklı   x  vektörlerini bulma  problemine, öz değer -öz vektör problemi ve skalerlerine de  A matrisinin  öz değerleri yada karekteristik değerleri denir.

Biz bu yazımızda özdeğerleri ve öz vektörleri pyton programlama ile nasıl çözeriz. Aslında özdeğer bulma işlemi çok uzun sürmektedir. Özellikle kuantum programlamada çok kullanılan özdeğer bulma işlemi pyton programlama ile çok kolay bir şekilde bulunmaktadır.

 

 

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