A particle limited to x axis has the wave frequency ax beyween x=0 and 1,0 elsewhere. Expectation value of particle position is
Answers
Answer:
a2/4
Explanation:
wave frequencyψ = axbetweenx= 0andx=1,ψ = 0elsewhere. The expectation valueof the particles position is.a)a2/4b)a2c)a2/2d)a2/8Correct answer is option 'A'. Can you explain this answer? is done on EduRev Study Group by Physics Students. The Questions and Answers of A particle limited to thex–axis has the wave frequencyψ = axbetweenx= 0andx=1,ψ = 0elsewhere. The expectation valueof the particles position is.
a2/4
Answer:
mark me brainlist
Explanation:
The Bohr theory of the atom has a number of severe limitations.
o It applies only to hydrogen and one-electron ions such as He+
and Li+2
.
o It cannot explain why certain spectral lines are more intense than others (that is, why
certain transitions between energy levels have greater probabilities of occurrence than
others).
o It cannot account for the observation that many spectral lines actually consist of several
separate lines whose wavelengths differ slightly.
o Perhaps most important, it does not permit us to obtain an understanding of how
individual atoms interact with one another to endow macroscopic aggregates of matter
with the physical and chemical properties we observe.
• A more general approach to atomic phenomena is required. Such an approach was
developed in 1925 and 1926 by Erwin Schrödinger, Werner Heisenberg, Max Born, Paul
Dirac, and others under the name of quantum mechanics.
5.1 QUANTUM MECHANICS
• Classical mechanics is an approximation of quantum mechanics
• The fundamental difference between classical (or Newtonian) mechanics and quantum
mechanics lies in what they describe.
o In classical mechanics, the future history of a particle is completely determined by its
initial position and momentum together with the forces that act upon it.
o Quantum mechanics also arrives at relationships between observable quantities, but the
uncertainty principle suggests that the nature of an observable quantity is different in the
atomic realm.
• In quantum mechanics, the kind of certainty about the future characteristic of classical
mechanics is impossible because the initial state of a particle cannot be established with
sufficient accuracy.
o The more we know about the position of a particle now, the less we know about its
momentum and hence about its position later.
• The quantities whose relationships quantum mechanics explores are probabilities.
o The Bohr theory states the radius of the electron’s orbit in a ground state hydrogen atom
is always exactly 5.3x10-11 m.
o Quantum mechanics states that this is the most probable radius. In a suitable experiment,
most trials will yield a different value, either larger or smaller, but the value most likely
to be found will be 5.3x10-11 m.
Wave Function
• The quantity with which quantum mechanics is concerned is the wave function Ψ of a body.
• The linear momentum, angular momentum, and energy of the body are other quantities that
can be established from Ψ.
• The problem of quantum mechanics is to determine Ψ for a body when its freedom of
motion is limited by the action of external forces.
• Wave functions are usually complex with both real and imaginary parts.
where A and B are real functions.
• A probability, however, must be a positive real quantity. The probability density |Ψ|2
for a
complex is therefore taken as the product of Ψ and its complex conjugate Ψ* which is Ψ*Ψ.
• The complex conjugate of any function is obtained by replacing i by -i wherever it appears
in the function.