Show that if qd≫1 the probability for tunneling through a potential barrier of width d is...

Show that if qd≫1 the probability for tunneling through a potential barrier of width d is proportional to e^(-2qd). Plot this function and explain the implications.

Expert Solution

genius_generous answered 2 years ago

There is no tunneling in the case of infinite potential barrier, but there is when we...

There is no tunneling in the case of infinite potential barrier, but there is when we have a finite well. In the classical analog, in the first case we have a particle bouncing between to infinitely rigid impenetrable walls and there is no tunneling, same as the quantum case. But if we have a finite barrier, means we have walls of finite rigidity, say made of cork or something. Then the particle would just break through some of the cork...

1(i) Show, if (X, d) is a metric space, then d∗ : X × X →...

1(i) Show, if (X, d) is a metric space, then d∗ : X × X → [0,∞) defined by d∗(x, y) = d(x, y) /1 + d(x, y) is a metric on X. Feel free to use the fact: if a, b are nonnegative real numbers and a ≤ b, then a/1+a ≤ b/1+b . 1(ii) Suppose A ⊂ B ⊂ R. Show, if A is not empty and B is bounded below, then both inf(A) and inf(B) exist and...

Let p be a prime and d a divisor of p-1. show that the d th...

Let p be a prime and d a divisor of p-1. show that the d th powers form a subgroup of U(Z/pZ) of order (p-1)/d. Calculate this subgroup for p=11, d=5; p=17,d=4 ;p=19,d=6

Branching Processes: Show that if μ=1 then probability of extinction is 1.

Show that the probability that all permutations of the sequence 1, 2, . . . ,...

Show that the probability that all permutations of the sequence 1, 2, . . . , n have no number i being still in the ith position is less than 0.37 if n is large enough. Show all your work.

How can we show that the VC dimension of a circle of dimension d is (d+1)

1. Let (X,d) be a metric space. Show that every open d-ball is a d-open subset...

1. Let (X,d) be a metric space. Show that every open d-ball is a d-open subset of X Show that every closed d-ball is a d-closed subset of X. 2: Let (X,d) be a metric space. Show that a subset A of X is d-open if and only if it is the union of a (possibly empty) set of open d-balls.

1. A moving particle with a charge of 6.52 is accelerated through a potential difference of...

1. A moving particle with a charge of 6.52 is accelerated through a potential difference of 234mV. Find the final velocity of the particle if its initial velocity is 5.24m/s. (mass of the charged particle=154g). 2. An unpolarized beam passes through a system containing three ideal polarizers. the first polarizer is oriented with a horizontal transmission axis, the second one has its transmission axis at 70.4degrees from the horizontal, and the third filter has a vertical transmission axis. What percent...

Given a normal distribution with μ=100 and σ= 10 complete parts (a) through(d)a.The probability that X>95...

Given a normal distribution with μ=100 and σ= 10 complete parts (a) through(d)a.The probability that X>95 is ____(please round to four decimal places as needed)b.The probability that X<90 is ____(please round to four decimal places as needed)c.The probability that X<80 or X> 125 is ____(please round to four decimal places as needed)d.90% of the values are greater than___ and less than___(please round to two decimal places as needed)

(1) The table below is a probability distribution of potential quantity of sales of Gourmet sausages...

(1) The table below is a probability distribution of potential quantity of sales of Gourmet sausages during a game. John Bull has to pay a concession fee of $200 to receive a permit to sell sausages at the stadium. Gourmet sausages can be bought at wholesale for $2.00 and sold in the stadium for $3.50 each. Unsold sausages cannot be returned. Given the probability distribution: How many sausages should John Bull expect to sell? How many sausages should John Bull...

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