Quantum Mechanics Answers

Obtain an expression of probability for finding the free particle at position x confined in a box of length a

An electron has the following wave function: ψ(x)=A(e^-x)(1-e^-x) Determine i) the normalization constant A, and ii) the expectation value of x .

Inside a spacecraft travelling at a speed of 0.8c with respect to the earth, the time interval between two events on the earth is measured to be 30 hrs. What would the time interval be if the spacecraft was travelling at a speed of 0.9c.

Formulate a one-dimensional model describing the dynamics of phytoplankton growth C(x, t)
in a water mass taking into account the following: D , its diffusion coefficient, a its rate of
growth, b its mortality rate due to sinking. Fixing the area of interest as 0 <[= x <=1 and the initial
concentration of phytoplankton as 20 moles / cm cube, find the concentration distribution of
phytoplankton in 0 <=x <=1 at any time t .

What are applications of free particles in continues state ?

What are applications of Schrödinger cat ?

What are Applications of Schrödinger cat ?

An electron has the following wave function:

ψ(x)=A(e^-x)(1-e^-x)


Determine
i) the normalization constant A, and
ii) the expectation value of x .

The frequency of the light emitted by a galaxy receding from the earth is measured
to be (1.5×10^3) MHz. Assuming that the wavelength of the light source is 22.5 cm,
calculate how fast the galaxy is receding from the earth?

A rocket is launched from a spaceship travelling with a speed of 0.8c towards the
earth. If the speed of the rocket is 0.6c, what would be its speed as observed by an
observer on earth if the rocket is moving
(i) towards the earth (ii) away from the earth?