Forwarded from Dev (卐 Ayhan)
#Quantum_Tunneling
Part 1
Imagine a box that you want to slide over a frictionless surface to the other side of a hill or peak. When the box reaches the top of the hill, its kinetic energy (K) converts to gravitational potential energy (U). If the box is right at the peak's tip, we denote its potential energy as Ub. Therefore, if the initial mechanical energy, or E = K + U, is greater than Ub, the box will pass over the peak. If it is less than that, the box cannot pass and will slide back down to the left of the peak.
So we say that this hill or peak acts as a barrier of potential energy or a potential barrier.
@Ayhan_Dev
Part 1
Imagine a box that you want to slide over a frictionless surface to the other side of a hill or peak. When the box reaches the top of the hill, its kinetic energy (K) converts to gravitational potential energy (U). If the box is right at the peak's tip, we denote its potential energy as Ub. Therefore, if the initial mechanical energy, or E = K + U, is greater than Ub, the box will pass over the peak. If it is less than that, the box cannot pass and will slide back down to the left of the peak.
So we say that this hill or peak acts as a barrier of potential energy or a potential barrier.
@Ayhan_Dev
Forwarded from Dev (卐 Ayhan)
#Quantum_Tunneling
Part 2
By solving the Schrödinger equation separately for the three regions: to the left of the barrier, inside the barrier, and to the right of the barrier, we arrive at some important points. The arbitrary constants that appear in the solutions must be chosen so that the values of ψ(x) and its derivatives with respect to x connect smoothly at the points x=0 and x=L. Then, by squaring the absolute value of ψ(x), we obtain the probability density.
The above figure shows a diagram of energy that includes two graphs for the previous situation:
1) The mechanical energy E of the electron is plotted when the electron is at any coordinate x<0.
2) The energy U of the electron, assuming that it reaches any value of x, is plotted as a function of the position x of the electron. The non-zero part of the graph (the potential barrier) has a height Ub and a thickness L.
@Ayhan_Dev
Part 2
By solving the Schrödinger equation separately for the three regions: to the left of the barrier, inside the barrier, and to the right of the barrier, we arrive at some important points. The arbitrary constants that appear in the solutions must be chosen so that the values of ψ(x) and its derivatives with respect to x connect smoothly at the points x=0 and x=L. Then, by squaring the absolute value of ψ(x), we obtain the probability density.
The above figure shows a diagram of energy that includes two graphs for the previous situation:
1) The mechanical energy E of the electron is plotted when the electron is at any coordinate x<0.
2) The energy U of the electron, assuming that it reaches any value of x, is plotted as a function of the position x of the electron. The non-zero part of the graph (the potential barrier) has a height Ub and a thickness L.
@Ayhan_Dev
Forwarded from ⚝ (Amir Hossein "Amiria" Maher)
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