mathematics

Illustrate the application of Fast Fourier Tyansform (FFT) through the following examples

Illustrate the application of Fast Fourier Tyansform (FFT) through the following examples: (a) Analysis the Power Spectral Density distribution for […]

Apr 21st, 2021

mathematics

Solve the initial value problem

( 30 marks) Solve the initial value problemx¨=_4x+3yy¨=2x_3yx(0)=0,y(0)=0,x_(0)=2,y_(0)=1 begin{aligned} ddot{x} &=-4 x+3 y \ ddot{y} &=2 x-3 y \ x(0)=0, […]

Apr 20th, 2021

mathematics

) Find the solution of the two-dimensional Laplace equation

(40 marks) Find the solution of the two-dimensional Laplace equationuxx+uyy=00

Apr 20th, 2021

mathematics

The wave function for a hydrogen atom in the ground state is given by

( 25 marks) The wave function for a hydrogen atom in the ground state is given by _(r)=Ae_r/aspsi(r)=A e^{-r / […]

Apr 20th, 2021

mathematics

The radial wave function for a hydrogen atom in the 3d state is given by

(25 marks) The radial wave function for a hydrogen atom in the 3d3 d3d state is given by R(r)=Ar2e__rR(r)=A r^{2} […]

Apr 20th, 2021

mathematics

The normalized wave function for a hydrogen atom in the 2s state is

( 25 marks) The normalized wave function for a hydrogen atom in the 2s2 s2s state is_2s(r)=132_a3(2_ra)e_r/2a psi_{2 s}(r)=frac{1}{sqrt{32 pi […]

Apr 20th, 2021

mathematics

Consider a simple model of the helium atom in which two electrons, each with mass m, move around the nucleus (charge +2e) in the same circular orbit.

( 25 marks) Consider a simple model of the helium atom in which two electrons, each with mass mmm, move […]

Apr 20th, 2021

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