. Evaluate the ground state energy of a harmonic oscillator of mass 'm' and angular frequency o'using the trial function. $(x) = { cos (2a) -a sxsa
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- V (x) = 00, V(x) = 0, x<0,x 2 a 0Consider a particle whose normalized wavefunction is given by p(x) = 2a/2xe x for x> 0 and p(x) = 0 for x < 0. a- For what values does the lp(x)[? have a peak? b- Calculate (x) and (x) - Calculate (p) and (p?) %3D %3D d- What is the probability that the particle is found between x = 0 and x = %3! e- Calculate the wavefunction in momentum space.Q3/1 Find the difference State in Second and first excited energies (AE) of Particle 1-D with length (L).Subject: Mathematical Physics Topic: Functions of a complex variable.Q.3 What is zero-point energy? If a classical oscillator has energy 1/2 ℏ w, what is its amplitude?n=2 35 L FIGURE 1.0 1. FIGURE 1.0 shows a particle of mass m moves in x-axis with the following potential: V(x) = { 0, for 0Q3: For a quantum harmonic oscillator in its ground state. Find: a) (x) b) (x²) с) ОхConsider a weakly anharmonic a 1D oscillator with the poten- tial energy m U(x) = w?a² + Ba* 2 Calculate the energy levels in the first order in the small anharmonicity parameter 3 using TIPT and the ladder operators.. (1) Find the kinetic, potential and total energies of the hydrogen atorn in the 2nd excited level.