Question

the electric potential of a hydrogen atom is modeled by the equation where a0 is the bohr radius of the atom and q is the charge of the proton. the electric field due to the hydrogen atom is assumed to be spherically symmetric (a) calculate the θ (theta) component of the electric field (6 pts) (b) calculate the ɸ (phi) component of the electric field (6 pts) (c) calculate the r (radial) component of the electric field (6 pts) (d) what is the change in the magnitude of the electric field if a test point moves from the position (7 pts) to the position problem 7 (25 pts) v (r)

Answer 1

In light of this, V=V 0 loge (r/r 0 ) Field E= dr dV =V 0(r0r) eE= r mV2 alternatively, reV0r0=rmV2. V=(m eV 0 r 0 ) \ s1 / 2mV=(m e V 0 r 0 ) 1/2 = constant mvr= 2 nh, also known as Bohr's quantum condition or Hermitian matrix.

Show that the eigenfunctions for the Hermitian matrix in review exercise 3a can be normalized and that they are orthogonal.  

Demonstrate how the pair of degenerate eigenvalues for the Hermitian matrix in review exercise 3b can be made to have orthonormal eigenfunctions.

Under the given Hermitian matrix, "border conditions," solve the following second order linear differential equation: d2x/ dt2 + k2x(t) = 0 where x(t=0) = L and dx(t=0)/ dt = 0.

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