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QUESTION 1: In quantum mechanics, the behaviour of a quantum particle (like an electron, for example) is described by the Schrödinger equation. The time-independent Schrödinger equation can be written in operator notation as H{y(x, y, z))-Ey(x, y, z) where H is known as the Hamiltonian operator and is defined as h2 2m Here, is a positive physical) constant known as Plancks constant and m is the mass of the particle (also Just a constant). V(x,y,Z) is a real-valued function. The dependant variable. ψ(x,y, z), describes the “quantum state (something analogous to the spatial location of the particle). More specifically, ^(x,y,z) is a probabilistic description of how likely you are to find the particle in a given region of space. If >(x,y,z) is subject to homogeneous Dirichlet boundary conditions in each independent variable on a domain [O.L]. show that the Hamiltonian operator, H, is symmetric. What can you conclude about a linear of symmetric operators?

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