The Double Slit Experiment and Quantum Mechanics∗
... single slit patterns. These patterns are so much alike that their sum looks just like the single slit pattern in Figure 2. It seems that detecting which slit they go through forces them to go through one slit or the other and also forces them to produce two single slit patterns instead of a double s ...
... single slit patterns. These patterns are so much alike that their sum looks just like the single slit pattern in Figure 2. It seems that detecting which slit they go through forces them to go through one slit or the other and also forces them to produce two single slit patterns instead of a double s ...
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... communication rests, admits to only two possible states: a classical on-off system must be in either state 0 or state 1, representing a single bit of information. Quantum mechanics is quite different. A two-level quantum system—the reader unfamiliar with basic quantum mechanics should consult the Ap ...
... communication rests, admits to only two possible states: a classical on-off system must be in either state 0 or state 1, representing a single bit of information. Quantum mechanics is quite different. A two-level quantum system—the reader unfamiliar with basic quantum mechanics should consult the Ap ...
QUANTUM ALGORITHMS FOR ELEMENT DISTINCTNESS∗ 1
... quantum computer, in contrast to the classical case. In Section 4, we consider the case where f is ordered (monotone non-decreasing): f (1) ≤ f (2) ≤ · · · ≤ f (N ). In this case, the quantum complexity of claw-finding and collision finding drops from O(N 3/4 log N ) to O(N 1/2 log N ). In Section 5 ...
... quantum computer, in contrast to the classical case. In Section 4, we consider the case where f is ordered (monotone non-decreasing): f (1) ≤ f (2) ≤ · · · ≤ f (N ). In this case, the quantum complexity of claw-finding and collision finding drops from O(N 3/4 log N ) to O(N 1/2 log N ). In Section 5 ...
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... fraction of the domain that is mapped to y. Below we describe the connection between these two approaches. e Suppose we sample P n times, and estimate each probability P(y) by the fraction P(y) of times y occurs among the n outcomes. We will analyze how good an estimator this is for P(y). For all j ...
... fraction of the domain that is mapped to y. Below we describe the connection between these two approaches. e Suppose we sample P n times, and estimate each probability P(y) by the fraction P(y) of times y occurs among the n outcomes. We will analyze how good an estimator this is for P(y). For all j ...
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.