Solution 1:
The wave function of the one-dimensional quantum particle
a>0 and it is constant in unit of length.
a) We have to find the average position of the particle.
The general equation of the average position of the particle
)
The most likely position of the particle is the value of x for which is the maximum.
So, the value of x = a.
c)
The average momentum of the particle
For the ground state of the quantum oscillator,
=0
Solution 2:
a)
We know that the Schrodinger wave equation is
Now, the separation of the variable be
Now,
) We know that the simple harmonic equation,
Now,
Solution 3:
The operators are A and B,
a)
It will be physically observable if, AB-BA=0
)
We can not measure the value of A and B if
In this case we can not measure the physical observables, co
esponding A and B together.
It means, if we measure the exact potion, then we will not be able to measure the momentum but if we measure the momentum, then we will not able to measure the exact position.
c) Now,
Solution 4:
Given,
We know that,
Solution 5
Given,
Speed of sound
Lattice constant
Solution 6:
Given,
Bandwidth of the lowest energy band = 1eV
Lattice constant (a)=3A
Solution 7:
Solution 8:
Given,
Atomic mass of U-238 = 238.051amu
Mass of Thorium-234 = 234.044 amu
Mass of alpha particle = 4.002 amu
Speed of alpha...