Quantum tunneling refers to the instance when a particle breaks through a barrier that is normally impassible. The basis of Quantum tunneling and how it functions can be summed up in this equation: (change in E)(change in t) = h. Although we can't change the total amount of energy without violating the law of conservation of energy, we can "borrow" some energy (change in E) to get over the barrier as long as we repay it in time: (change in t) = h / (change in E). The reason a particle can do this is that we cannot accurately know the energy of a particle. It is instead expressed as an uncertainty: (change in E) = h / (change in t). Of course, if the barrier is too wide or tall, the chances of quantum tunneling occurring becomes scare because of the increased time needed needed to repay the amount of energy borrowed. (Quantum Universe)

Funnily enough, waves share a quantum tunneling like component to them as well. If we were to increase the angle above a glass block's critical angle, we achieve total-internal reflection caused by a standing wave that does not transmit any light energy. This means all of the light that would exit the glass block before the critical angle is instead kept within the glass block, hence the name. If we were to place another glass block next to the existing one with the total-internal reflection, you will see that light somehow travels into the added block, even though there is supposed to be total-internal reflection. The reason for that is the amplitude of the standing wave in the "forbidden" gap hasn't fully decayed. This phenomena is referred to as frustrated total-internal reflection. (Quantum Universe)

The Scanning Tunneling Microscope (STM) works almost in the same way as the light waves do. The machine takes advantage of the "vacuum tunneling" property of electrons in order to study the surface of materials. Electrons in a solid have a small chance of appearing outside of the metal surface. Much like the...

...QuantumTunneling
Free Wave Packet
Tunneling through a Barrier
Tunneling over a Well
Example: Tunneling Microscope
Tunnel Transistor
-particle decay
QuantumTunneling
Postulates
Maybe in lab
2
QuantumTunneling
Time Dependent Wave Equation
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What is the assumption Junior?
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3
QuantumTunneling
Free Wave Packet in One Dimension
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For one-dimension we have
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Recall we make up a wave
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4
QuantumTunneling
Potential Step Barrier
The energy can be greater or less than...

...What are we made of???
Throughout the years the Quantum Mechanic model has evolved many times. This evolution has taken place after every major discovery in Quantum Mechanics. The current Quantum mechanic model is by far the most accurate example of an atom and how it works. Currently the model depicts a proton (or more than one depending on the atom) and neutron in the nucleus and a an electron rotating around the nucleus in an energy level, or an estimated path of the electron.
The first person to purpose the existence of atoms was Democritus. Democritus’ had the right idea however the details of his original theory were not quite right. Democritus believed there was a select few elements and the ratio between these elements made up matter. It was free thinking individuals like this that led to the discovery of several theories that aloud atoms to be tested.
François Bacon was one of those individuals. He saw a need for organization in the scientific community. His answer to this was the scientific method. The scientific method was a list of steps that helped organize experiments.
Antoine Lavoisier was a French nobleman that had made a hobby of chemistry. However because of this bored tax collector with a passion we were able to accurately test countless theories. Lavoisier created the “Law of Conservation of Matter,” which stated that no matter could be created or destroyed. This Law caused a flurry of questions, were did...

...one of the following atoms or ions would the 2s and 2p orbitals have the same energy? a) O2– b) H c) He d) Li+ e) F6+
5. Which of the following electron excitations of the hydrogen atom requires light of the shortest wavelength? a) b) c) d) e) n = 2 to n = 3 n = 3 to n = 4 n = 4 to n = 20 n = 5 to n = 100 n = 4 to n = 1000
6. Which one of the following electron configurations is not valid? a) 1s2 2s2 2p2 b) 1s2 2s2 2p6 3s2 3p6 c) 1s2 2s2 2p6 3s2 3p2 d) 1s2 2s2 2p6 3s2 3p3 e) 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p8
7. What is the specific activity (in Bq g–1) of the nuclide 1.6 seconds? a) 2.9 1021 b) 3.3 1021 c) 3.6 1021
90 35
Br , whose half-life is
d) 1.0 1021
e) 2.6 1023
8. Which one of the following sets of quantum numbers is valid? n a) b) c) d) e) 3 1 3 1 5 l 1 1 3 1 4 ml (or m) 0 0 –2 1 3 ms (or s) 0 –½ +½ 0 +½
9. Which of the following lobe depictions of atomic orbitals is the best representation of a 1s orbital? The white and grey shading represent different phases of the wavefunction.
a)
b)
c)
d)
e)
10. How many nodes does a 5s atomic orbital have? a) b) c) d) e) 0 planar nodes and 0 spherical nodes 3 planar nodes and 2 spherical nodes 1 planar node and 1 spherical node 0 planar nodes and 4 spherical nodes 2 planar nodes and 3 spherical nodes 1C, 2C, 3E, 4B, 5A, 6E, 7A, 8E, 9D, 10D
Correct answers:
...

...difference between classical and quantum physics and why classical physics does not work on quantum level particles?” First of all what is classical and quantum physics, Classical physics is the physics of the world we see around us; classical physics is the physics of the objects that we can feel or see. Quantum physics starts when every thing gets as small as (the size), quantum physics tells use about the behaviors and interaction of subatomic particles and more about quantum physics will be uncovered in this essay.
I have always been fascinated by quantum physics, how it is so different to the world we see and that there is so little we can relate between each other, The laws of physics changes dramatically when you change to quantum states. It is like it is another world, a different dimension. I will be looking at the differences and similarities of classical and quantum energies of different objects. This will be done by looking at the total energy of objects from a bowling ball to a electron, to calculate the total energy of these objects I will be using the classical physics formula for total energy of an object (E=12mv2+mgh) and Schrödinger’s equation HΨ=EΨ.
I believe that the question that I will be researching will give me a good introduction to quantum physics and by using Schrödinger’s equation will also give me a...

...The Impossibility of Quantum Teleportation due to Heisenberg’s Principle of Uncertainty
The classical concept of teleportation is simple in theory, but much harder in practice. Imagine two boxes; namely Box A and Box B. The aim is simply to get the contents of Box A into Box B. This is done by gathering all the information of the contents of Box A and sending it to Box B, where the information may be used to recreate it. In theory this is quite simple, ignoring the low supply of sophisticated, giant 3D printers. One could take as elementary measurements of the contents of Box A as wished (in accordance to the complexity of the contents) and at the other end it could be recreated. One would then destroy the original, and like that, the contents have been “teleported” from Box A to Box B. There is not transfer of matter or energy, simply information. However, this is not quite teleportation. It may seem like it on simple objects, such as something mundane like a wooden plank with the same dimensions and spider-man logo on the side, but if we were to try to teleport something more complex such as a living thing, we would find that the product would be nothing the same, if alive at all. A common definition of teleportation goes as follows:
“Teleportation is the name given by science fiction writers to the feat of making an object or person disintegrate in one place while a perfect replica appears somewhere else” [1]
This definition of teleportation...

...The Quantum Mechanical Model of the Atom
Energy Is Quantized
After Max Planck determined that energy is released and absorbed by atoms in certain fixed amounts known as quanta, Albert Einstein took his work a step further, determining that radiant energy is also quantized—he called the discrete energy packets photons. Einstein’s theory was that electromagnetic radiation (light, for example) has characteristics of both a wave and a stream of particles.
The Bohr Model of the Atom
In 1913, Niels Bohr used what had recently been discovered about energy to propose his planetary model of the atom. In the Bohr model, the neutrons and protons are contained in a small, dense nucleus, which the electrons orbit in defined spherical orbits. He referred to these orbits as “shells” or “energy levels” and designated each by an integer: 1, 2, 3, etc. An electron occupying the first energy level was thought to be closer to the nucleus and have lower energy than one that was in a numerically higher energy level. Bohr theorized that energy in the form of photons must be absorbed in order for an electron to move from a lower energy level to a higher one, and is emitted when an electron travels from a higher energy level to a lower one. In the Bohr model, the lowest energy state available for an electron is the ground state, and all higher-energy states are excited states.
Orbitals and Quantum Numbers
In the 1920s, Werner Heisenberg put forth his...

...Drion Shkreli
Alchemy to Astrophysics
Professor Efthimiades
12/11/2012
Quantum Mechanics Homework
1. Principles of Quantum Mechanics
a. Particles have multiple virtual motions and each motion is accompanied by a wave. The strength of the total particle wave at each point corresponds to the probability that the particle may be found there. Applying this principle we can explain all kinds of phenomena, from the properties of atoms and radioactivity to light reflection.
2. Electron Double Slit Experiment
a. Electrons are fired (possibly one at a time) toward a screen with two slits and each electron that passes through leaves a dot on a film plate. The dots accumulate on specific places, as shown in the diagram below, separated by b lank zones. Therefore, there is a certain probability that an electron may land on C, E, G… and zero probability that it may go to D, F…
b. The probability that an electron may land on some point on the film arises from the interference of two electron virtual waves meeting at that point, one coming from the top slit and the other from the bottom slit. The interference of the infinite electron waves fanning out of the slits produces a succession of high and low intensities of the electron wave function on the film that corresponds to highs and lows of the probability of where the electron may end up.
3. Tunneling
a. This is when a particle can pass...

...Quantum Numbers
Quantum Numbers
The Bohr model was a one-dimensional model that used one quantum number to describe the distribution of electrons in the atom. The only information that was important was the size of the orbit, which was described by the n quantum number. Schrödinger's model allowed the electron to occupy three-dimensional space. It therefore required three coordinates, or three quantum numbers, to describe the orbitals in which electrons can be found.
The three coordinates that come from Schrödinger's wave equations are the principal (n), angular (l), and magnetic (m) quantum numbers. These quantum numbers describe the size, shape, and orientation in space of the orbitals on an atom.
The principal quantum number (n) describes the size of the orbital. Orbitals for which n = 2 are larger than those for which n = 1, for example. Because they have opposite electrical charges, electrons are attracted to the nucleus of the atom. Energy must therefore be absorbed to excite an electron from an orbital in which the electron is close to the nucleus (n = 1) into an orbital in which it is further from the nucleus (n = 2). The principal quantum number therefore indirectly describes the energy of an orbital.
The angular quantum number (l) describes the shape of the orbital. Orbitals have shapes that are best described as...