Writing Assignment 2

Writing Assignment 2 - eigenvector for softness,...

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Rabbit Troop Andrew Dixon, Stephen Beckley, Seta Degann Writing Assignment #2 In the vector space formalism of quantum mechanics, the current state of the electron can be represented by a vector called a “state vector”. If the state vector for the property we are trying to observe is an eigenvector of the operator of that property, the eigenvalue of the state vector reveals the state of the electron. For instance, if the hardness operator were H, and the state vector of an electron were |h>, then H|h>=g|h>, were g is a scalar; g would therefore be the hardness value of the electron. We will continue using H as the hardness operator, and will introduce C as the color operator. We will use |h> for the eigenvector for hardness, |s> for the
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Unformatted text preview: eigenvector for softness, |w> for the eigenvector for white, and |b> as the eigenvector for black. So now we can use |h> and |s> as a basis for H and |w> and |b> as a basis for C (assuming the operators are 2x2). This means we can represent |w> and |b> as linear combinations of |h> and | s> and vice versa. |w> and |b> are not eigenvectors for H (as they are a linear combination of both |h> and |s>), so this means that there is no eigenvalue for |w> and |b>, which means that there is no definite hardness value, which is the mathematical representation of superposition. The same is true with |h> and |s> with respect to C. So hardness and color, in a sense, are incompatible qualities....
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