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Abstrak :
Kuantisasi Dirac merupakan suatu prosedur yang digunakan untuk mengkuantisasi sistem terkonstrain. Lagrangian yang akan dikuantisasi adalah Lagrangian sistem kuantum (fermion) terkonstrain. Namun ada problem yang muncul dalam proses kuantisasi Lagrangian sistem tersebut. Problem tersebut ialah kerapatan Hamiltonian sistem mengandung variabel turunan terhadap waktu. Hal tersebut diakibatkan karena Lagrangian sistem mengandung variabel turunan orde kedua terhadap waktu. Problem tersebut akan menyulitkan kita dalam perhitungan relasi Poisson braket antara variabel sistem. Untuk mengatasi hal tersebut dilakukan transformasi medan (pendekatan) pada Lagrangian sistem, agar Lagrangian sistem tidak mengandung turunan orde kedua terhadap waktu. Sehingga, kerapatan Hamiltonian kanonik tidak lagi mengandung variabel turunan terhadap waktu. Dengan menggunakan prosedur Dirac, kita akan memperoleh Hamiltonian primer sistem yang siap untuk dikuantisasi. ......Dirac Quantization is a procedure that is used to quantize a constraint system. Lagrangian that will be quantized is a Lagrangian of constraint quantum system (fermion system). But there is a problem in quantizaton process of the Lagrangian of the system. The problem is there are exist firrst order time derivative variables in the Hamiltonian density. It is caused by the fact that the Lagrange equation of the system has the second order derivatives. So, the problem will generate difficulty in the Poisson brakect relation between variables of the system. To solve this problem, the field transformation to the system Lagrange equation is used, so the Lagrange equation now does not consist of second order derivatives variables. As a result, the Hamiltonian density is free from the derivatives variables anymore. By using Dirac procedure, we will get the primary Hamiltonian of the system that is ready quantized.

Abstrak :
Self-adjoint extensions in quantum mechanics begins by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes of the naïve treatment. The necessary mathematical background is then built by developing the theory of self-adjoint extensions. Through examination of various quantum-mechanical systems, the authors show how quantization problems associated with the correct definition of observables and their spectral analysis can be treated consistently for comparatively simple quantum-mechanical systems. Systems that are examined include free particles on an interval, particles in a number of potential fields including delta-like potentials, the one-dimensional Calogero problem, the Aharonov–Bohm problem, and the relativistic Coulomb problem.