Probability of Finding Particles

If a hydrogen atom is in the ground state, what is the probaility of finding the electron in a volume of 1.0 pm^3 at a distance of 52.9 pm from the nucleus, in a fixed but arbitrary direction? note: 1 pm = 10^-12 m

Calculation for finding probablility of electron in hydrogen atom

Calculate the probablility that the electron in the ground state of the hydrogen atom will be found outside the first bohr radius (a0).

Attempt to apply quantum mechanics to macroscopic objects

A small object of mass 1.00mg is confined to move between two rigid walls separated by 1.00cm (infinite square well approximation). a) Calculate the minimum speed of the object. b) If the speed of the object is 3.0cm/s, find the corresponding value of n (the quantum number).

Anti-hermitian operator

This is problem 3.26 in Griffiths' Introduction to Quantum Mechanics (second editition): An anti-hermitian (or skew-hermitian) operator is equal to minus its hemitian conjugate: (a) Show that the expectation value of an anti-hermitian operator is imaginary. (b) Show that the commutator of two hermitian operators is anti-hermitian. How about the commutator of two anti-hermitian operators?

Velocity; Space; Direction etc ...

Please assist me with the attached questions. Thanks. Attached: 1) Galaxy A is found to be receding from us with a speed of 0.8c. Galaxy B I found to be receding from us with a speed of 0.4c. (a) What is our velocity as seen from galaxy A? (b) What is velocity of galaxy B as seen from galaxy A, if both are seen in the same direction in space? (c) What is the velocity of galaxy B as seen from galaxy A, if they are seen in exactly opposite directions in space? ... {see attachment for complete list}