By Einstein

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**Sample text**

The spin of the electron is like the spin of the earth around its axis (which takes 24 hours to complete a turn). In quantum mechanics, apart from the spatial degrees of freedom of elementary particles, an inner degree of freedom called “spin” exists. We say that a particle has spin s if it can have 2s + 1 projections of its spin on an external axis. , the spin states |↑ and |↓ can be represented by two-component vectors |↑ ≡ 1 , 0 |↓ ≡ 0 . , the projection of the angular momentum on an external axis (say, the z-axis) can take the values +1, 0, and −1 (in units of h¯ ), and these three states can be represented by three-dimensional vectors, as will be discussed in Chapter 3.

A basic building block of all electronics today is the transistor, a semiconductor device that uses a small amount of voltage or electrical current to control a larger voltage or current. For example, a transistor can be used to set the voltage on a wire to be either high or low, representing a binary 1 or 0, respectively. Transistors can have very fast response (as fast as 10−11 s, or 100 GHz), and are used in a very wide variety of applications: amplification, switching, signal modulation, etc.

One can ask whether it is possible to put a macroscopic system (or if you like, a macroscopic object) into a superposition state. In Schr¨odinger’s famous cat paradox, the question asked is whether one can put a cat into a superposition state |ψ cat = √1 (|ψalive + |ψdead ). In this state, the cat is neither alive nor dead, but is in a linear combination of the 2 two (until we perform a measurement and collapse the cat’s wave function, see Sec. 4; if we find the cat to be dead, we would be responsible for its death because we carried out the measurement).