(b) (ii) Prove that gik is a symmetric contravariant tensor of rank two.
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- I need the answer as soon as possibleA particle of mass m in a certain force field given by F the force. Calculate the time it will take the particle to move from a point at a distance D from the - klx is moving toward the center of center to the center of the force.If A, B and C are Hermitian operators then 1 2i verfy whether the relation Hermitian or not. [AB] is
- In Poincare transformation if scalar field is invariant under translation, then prove that generator of translation is momentum 4 vector.(7) Suppose the Hamiltonian for a particle in three dimensions is given by H = +V(f). Here, the 2m operator î represents the radial direction relative to the origin of coordinates. In other words, the potential energy exhibits spherical symmetry. Show that the three operators, H, L.,Ľ commute.(c) Consider any linear bounded operator B : H →H i. Show that B - B¹ is anti-Hermitian and  + B¹ is Hermitian. ii. Show that B can be expressed as a linear combination of a Hermitian and an anti-Hermitian operator.
- 2-) Hamiltonian operator 1 1 (pỉ + p²) +÷mw²(x? + x3) 2m Consider a system with two identical particles. Find the energy spectrum of the system and determine its degeneracy discuss.(a) Using Dirac notation, write down the definition of a projection operator and that of a density operate and state the differences between the two.The Hamiltonian matrix has been constructed using an orthonormal basis. (1 1 0V (1 0 1) A = (2 1 0 )+(0 2 2 \2 1 4 where H = Hº + V and cis a constant. 1 2 0/ b) Use time-independent perturbation theory to determine the eigenvalues with corrections up to second order.