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Tunneling through arbitrary potential barrier Consider the tunneling problem in the WKB approximation through an arbitrary...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width L represented by a step function ſo I<0 or 1>L V U. r>0 and 2<L The total wavefunction is subject to the time-independent Schrödinger equation = EV (2) 2m ar2 +V where E is the energy of the quantum particle in question and m is the mass of the quantum particle. A The total wavefunction of a free particle that enters the barrier from...
3. The process of alpha-radioactivity is an example of a barrier tunneling phenomenon, which can be...
3. The process of alpha-radioactivity is an example of a barrier tunneling phenomenon, which can be envisioned as an alpha particle trapped inside a nucleus by a "Coulomb Barrier" produced by the combination of the attractive nuclear force that exists inside the nucleus, and the repulsive Coulomb force. A very crude picture of this situation is shown in the picture below, where we make the approximation that the alpha particle must tunnel through a square potential barrier to escape the...
18. Consider the potential barrier as shown in the figure. Calculate the transmission coefficcient. Discuss the...
18. Consider the potential barrier as shown in the figure. Calculate the transmission coefficcient. Discuss the depence of this coefficient. This is so called tunneling effect. Give a physical phenomenum that can be explained by this fact. E 00 0 V1 V(x) = x < 0 -V 0 < x <a V2 a< x <b 0 x <b
In class we considered quantum tunneling of a particle of energy Eo through a barrier of...
In class we considered quantum tunneling of a particle of energy Eo through a barrier of potential Vofor Vo > Eo. Here we focus on two aspects of the problem we ignored in class. In order to simplify we will only consider the initial first half of the barrier as shown below RegionI xS0 Regionx 20 Il There are two cases to consider: Eo< Vo Considered in class E>Vo Not considered in class Here we will focus on the second...
plz hlp Tunneling An electron of energy E = 2 eV is incident on a barrier...
plz hlp
Tunneling An electron of energy E = 2 eV is incident on a barrier of width L = 0.61 nm and height Vo-3 eV as shown in the figure below. (The figure is not drawn to scale.) 1) What is the probability that the electron will pass through the barrier? The transmission probability is 0 SubmitHelp 2) Lets understand the influence of the exponential dependence. If the barrier height were decreased to 2.8 eV (this corresponds to only...
4. An electron having total energy E 4.50 eV approaches a rectangular Energy energy barrier with...
4. An electron having total energy E 4.50 eV approaches a rectangular Energy energy barrier with U= 5.00 eV and L = 950 pm as shown. Classically, the electron cannot pass through the barrier because E < U. However, quantum mechanically the probability of tunneling is not zero. a) Calculate this probability, which is the transmission coefficient. b) By how much would the width L of the potential barrier have to change for the chance of an incident 4.50-eV electron...
Consider the finite rectangular barrier described by the potential: where Vo is a real and positive...
Consider the finite rectangular barrier described by the potential: where Vo is a real and positive constant. 1. How many bound states does this potential admit? 2. Find the transmission coefficient for a scattering state with energy E Vo 0
mechani mie The potential energy barrier shown below is a simplified model of thec electrons in...
mechani mie The potential energy barrier shown below is a simplified model of thec electrons in metals. The metal workfunction (Ew), the minimum energy required to remove an electron from the metal, is given by Ew-,-E where 1s the height of the potential energy barrier and E is the energy of the electrons near the surface of the metal. The potential energy barrier is = 5 eV V(x) V=0 (a) The wavefunction of an electron on the surface (x< 0)...
2. An electron with energy E= 1 eV is incident upon a rectangular barrier of potential...
2. An electron with energy E= 1 eV is incident upon a rectangular barrier of potential energy Vo = 2 eV. About how wide must the barrier be so that the transmission probability is 10-37 Electron mass is m=9.1 x 10-31 kg. (Hint: note the word "about". A quick sensible approximation is accepted for full credit. The exact calculation is feasible in an exam, but long and perilous - avoid at all costs.]
Scattering #1 Consider the "downstep" potential shown. A particle of mass m and energy E, inciden...
Scattering #1 Consider the "downstep" potential shown. A particle of mass m and energy E, incident from the left, strikes a potential energy drop-off of depth Vo 0 (2 pts) Using classical physics, consider a particle incident with speed vo. Use conservation of energy to find the speed on the right vf. ALSO, what is the probability that a given particle will "transmit" from the left side to the right side (again, classically)? A. B. (4 pts) This problem is...
(III) Quantum Tunneling Consider an electron in 1D in presence of a potential barrier of width L represented by a step function ſo I<0 or 1>L V U. r>0 and 2<L The total wavefunction is subject to the time-independent Schrödinger equation = EV (2) 2m ar2 +V where E is the energy of the quantum particle in question and m is the mass of the quantum particle. A The total wavefunction of a free particle that enters the barrier from...
3. The process of alpha-radioactivity is an example of a barrier tunneling phenomenon, which can be envisioned as an alpha particle trapped inside a nucleus by a "Coulomb Barrier" produced by the combination of the attractive nuclear force that exists inside the nucleus, and the repulsive Coulomb force. A very crude picture of this situation is shown in the picture below, where we make the approximation that the alpha particle must tunnel through a square potential barrier to escape the...
18. Consider the potential barrier as shown in the figure. Calculate the transmission coefficcient. Discuss the depence of this coefficient. This is so called tunneling effect. Give a physical phenomenum that can be explained by this fact. E 00 0 V1 V(x) = x < 0 -V 0 < x <a V2 a< x <b 0 x <b
In class we considered quantum tunneling of a particle of energy Eo through a barrier of potential Vofor Vo > Eo. Here we focus on two aspects of the problem we ignored in class. In order to simplify we will only consider the initial first half of the barrier as shown below RegionI xS0 Regionx 20 Il There are two cases to consider: Eo< Vo Considered in class E>Vo Not considered in class Here we will focus on the second...
plz hlp
Tunneling An electron of energy E = 2 eV is incident on a barrier of width L = 0.61 nm and height Vo-3 eV as shown in the figure below. (The figure is not drawn to scale.) 1) What is the probability that the electron will pass through the barrier? The transmission probability is 0 SubmitHelp 2) Lets understand the influence of the exponential dependence. If the barrier height were decreased to 2.8 eV (this corresponds to only...
4. An electron having total energy E 4.50 eV approaches a rectangular Energy energy barrier with U= 5.00 eV and L = 950 pm as shown. Classically, the electron cannot pass through the barrier because E < U. However, quantum mechanically the probability of tunneling is not zero. a) Calculate this probability, which is the transmission coefficient. b) By how much would the width L of the potential barrier have to change for the chance of an incident 4.50-eV electron...
Consider the finite rectangular barrier described by the potential: where Vo is a real and positive constant. 1. How many bound states does this potential admit? 2. Find the transmission coefficient for a scattering state with energy E Vo 0
mechani mie The potential energy barrier shown below is a simplified model of thec electrons in metals. The metal workfunction (Ew), the minimum energy required to remove an electron from the metal, is given by Ew-,-E where 1s the height of the potential energy barrier and E is the energy of the electrons near the surface of the metal. The potential energy barrier is = 5 eV V(x) V=0 (a) The wavefunction of an electron on the surface (x< 0)...
2. An electron with energy E= 1 eV is incident upon a rectangular barrier of potential energy Vo = 2 eV. About how wide must the barrier be so that the transmission probability is 10-37 Electron mass is m=9.1 x 10-31 kg. (Hint: note the word "about". A quick sensible approximation is accepted for full credit. The exact calculation is feasible in an exam, but long and perilous - avoid at all costs.]
Scattering #1 Consider the "downstep" potential shown. A particle of mass m and energy E, incident from the left, strikes a potential energy drop-off of depth Vo 0 (2 pts) Using classical physics, consider a particle incident with speed vo. Use conservation of energy to find the speed on the right vf. ALSO, what is the probability that a given particle will "transmit" from the left side to the right side (again, classically)? A. B. (4 pts) This problem is...
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