16. A particle has the following wavefunction:L) from x = 0 to x = L, and yeverywhere else.Ax(x(a) What is the value of A?(b) What is the probability of finding the particlein the region 0 < x < L/2? (You can calculatethis, but you can also figure it out with nocalculations by making a graph.)-== 0(c) What is the probability of finding the particlein the region 0 < x < L/4? (This one you haveto calculate, although a graph can be a greatreality check.)

Answered: Image /qna-images/answer/8b94bc7a-cc31-4079-8b7d-eb120e27ef35.jpg

Answered: Ax(x L) from x = 0 to x = L, and y <=0…

Similar questions

Show that at high enough temperatures (where KBT » ħw) the partition function of a simple quantum mechanical harmonic oscillator is approximately Z≈ (Bħw)-¹ Then use the partition function to calculate the high temperature expressions for the internal energy U, the heat capacity Cy, the Helmholtz function F and the entropy S.
Suppose we had a classical particle in a frictionless box, bouncing back and forth at constant speed. The probability density of the position of the particle in soma box of length L is given by: 0 ans-fawr (7) p(x)= 0 x L a. Sketch the probability density as a function of position b. What must A be in order for p(x) to be normalized? Remember that you are welcome to use resources to solve integrals such as Wolfram Alpha, a table of integrals etc.
No Spacing Heading 1 Normal Aa v A A 困、 Paragraph Styles The action along a path is defined to be: S = [(K.E.-P. E.) dt Determine the physical units of action. Detail Feynman's approach to calculating the probability amplitude for an electron to go from one event A to another B using the "sum over all paths". A'Focus 12 1> 12
If the Probability of each of the steps of the drunk man is equal (p = q = 1/2) obtain the Probability that act of 5 steps 3 of them would be to the right. . Calculate the relative width for random walk problem. if the total number of steps is N = 25 a. for equal number of steps to the right and left side (p = q) . b. for p = 0.4 , q = 0.6
Determine the expectation values of the position (x) (p) and the momentum 4 ħ (x)= cos cot,(p): 5V2mw 4 mah 5V 2 sin cot 2 ħ moon (x)= sin cot, (p)= COS at 52mo 2 4 h 4 moh (x)= 52mo sin cot.(p) COS 2 h s cot, (p) 5V2mco 2 moh 5V 2 sin of as a function of time for a harmonic oscillator with its initial state ())))
(d) Prove that for a classical particle moving from left to right in a box with constant speed v, the average position = (1/T) ff x(t) dt = L/2, where T L/v is the time taken to move from left to right. And = : (1/T) S²x² (t) dt L²/3. Hint: Only consider a particle moving from left x = 0 to right x = L = and do not include the bouncing motion from right to left. The results for left to right are independent of the sense of motion and therefore the same results apply to all the bounces, so that we can prove it for just one sense of motion. Thus, the classical result is obtained from the Quantum solution when n >> 1. That is, for large energies compared to the minimum energy of the wave-particle system. This is usually referred to as the Classical Limit for Large Quantum Numbers.

Ax(x L) from x = 0 to x = L, and y <=0 everywhere else. (a) What is the value of A? (b) What is the probability of finding the particle in the region 0 < x < L/2? (You can calculate this, but you can also figure it out with no