A quantum system is composed of an electron in free movement in a region one- dimensional, between O and L = 1.00 x 10-1º m. Now consider that the system is subject to a potential given by V(x) = -€ sin(x/L), where ɛ = 6.00 x 10-20 J. With Based on First Order Perturbation Theory, calculate the energy of the state fundamental of the system and compare with the value obtained in the absence of the potential.

The Morse oscillator modeling a different diatomic molecule has D = 384 kJ/mole and hw = 1240 cm-¹. (Again, 11.9627 J/mole = 1 cm ¹.) ✓ нал (a) What is the energy of the pictured eigenfunction? Report the energy in cm¹ above the minimum in the potential well. (b) How close to the dissociation limit is this state in kJ/mole, that is, what is the energy difference between this state and molecular dissociation?

Consider 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.

We have a three dimensional vector space where |P1), |P2) and |23) form a complete orthonormal basis. In this vector space we have two states |a)=5i|1)+3i 2)+(-2+2i) 3) and |B) =4i|1)-5 i) Calculate (a and (B, in terms of the dual basis vectors (y|, (p2|, (P3|. ii) Calculate the inner/scalar products (alB) and (Ba). Show that (8|a) =(a|B)".