Quantum Engi Q and A_Part_8

Quantum Engi Q and A_Part_8 - 22 CHAPTER 3 BASIC IDEAS OF...

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22 CHAPTER 3. BASIC IDEAS OF QUANTUM MECHANICS 3.4.1 Only eigenvalues 3.4.2 Statistical selection 3.5 A Particle Confined Inside a Pipe 3.5.1 The physical system 3.5.2 Mathematical notations 3.5.3 The Hamiltonian 3.5.4 The Hamiltonian eigenvalue problem
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3.5. A PARTICLE CONFINED INSIDE A PIPE 23 3.5.5 All solutions of the eigenvalue problem 3.5.5.1 Solution piped-a Question: Write down eigenfunction number 6. Answer: Substituting n = 6 in the generic expression for the eigenfunctions, ψ n = radicalBigg 2 x sin parenleftbigg x x parenrightbigg you get ψ 6 = radicalBigg 2 x sin parenleftbigg 6 π x x parenrightbigg 3.5.5.2 Solution piped-b Question: Write down eigenvalue number 6. Answer: Substituting n = 6 in the generic expression for the eigenvalues, E n = n 2 ¯ h 2 π 2 2 mℓ 2 x you get E 6 = 36¯ h 2 π 2 2 mℓ 2 x 3.5.6 Discussion of the energy values 3.5.6.1 Solution pipee-a Question: Plug the mass of an electron, m = 9.109,38 10 31 kg, and the rough size of an hydrogen atom, call it x = 2 10 10 m, into the expression for the ground state kinetic energy
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