CHAPTER 6: Quantum Mechanics II
... In order to avoid multiple values of the probability, the wave function must be single valued. For finite potentials, the wave function and its derivative must be continuous. This is required because the second-order derivative term in the wave equation must be single valued. (There are exceptions t ...
... In order to avoid multiple values of the probability, the wave function must be single valued. For finite potentials, the wave function and its derivative must be continuous. This is required because the second-order derivative term in the wave equation must be single valued. (There are exceptions t ...
Reality Final: Why Ask Why?
... Newton's reign. The first blow was not a fatal one. The velocity of light was experimentally shown to be a constant, c. This gave Newtonian physics a maximum possible velocity (nothing can travel faster than light), equations were adjusted, and everything was still fine. Then, the Newtonian concept ...
... Newton's reign. The first blow was not a fatal one. The velocity of light was experimentally shown to be a constant, c. This gave Newtonian physics a maximum possible velocity (nothing can travel faster than light), equations were adjusted, and everything was still fine. Then, the Newtonian concept ...
ppt
... The Schrödinger equation describes the motion of a particle of mass m moving in a region where the potential energy is described by V(x). 2 y d -h 2 m dx2 + V(x) y = E y ...
... The Schrödinger equation describes the motion of a particle of mass m moving in a region where the potential energy is described by V(x). 2 y d -h 2 m dx2 + V(x) y = E y ...
Another version - Scott Aaronson
... Range(g) are either equal or disjoint. Decide which. In the “black-box” setting, this problem takes (2n/7) time even with a quantum computer (slight variant of the “collision lower bound” I proved in 2002). Even in non-blackbox setting, would let us solve e.g. Graph Isomorphism Theorem (Harlow-Hayd ...
... Range(g) are either equal or disjoint. Decide which. In the “black-box” setting, this problem takes (2n/7) time even with a quantum computer (slight variant of the “collision lower bound” I proved in 2002). Even in non-blackbox setting, would let us solve e.g. Graph Isomorphism Theorem (Harlow-Hayd ...
with x
... this is done by looking at the diffraction pattern of X-rays scattered off the material (see ch 27.4). Why are X-rays used for this and not for example visible light? a) the wavelength of X-rays is close to the spacing between atoms in a crystal b) since the frequency (and thus energy) of X-rays ...
... this is done by looking at the diffraction pattern of X-rays scattered off the material (see ch 27.4). Why are X-rays used for this and not for example visible light? a) the wavelength of X-rays is close to the spacing between atoms in a crystal b) since the frequency (and thus energy) of X-rays ...
Particle in a box
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example a ball trapped inside a large box, the particle can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never ""sit still"". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.The particle in a box model provides one of the very few problems in quantum mechanics which can be solved analytically, without approximations. This means that the observable properties of the particle (such as its energy and position) are related to the mass of the particle and the width of the well by simple mathematical expressions. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.