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2. Consider the so-called Pauli operators ôx = [0)(1| + |1)(0], ôy = −i|0)(1| +i|1)(0| and ôz = 0) (0||11], where {[0), [1}} form an orthonormal basis of the considered Hilbert space. (c) Solve the eigenvalues and the corresponding eigenstates of each Pauli operator using the matrix form, and write the eigenstates using the ket vectors [0) and |1). (d) For each Pauli operator, show that the eigenstates are orthogonal.

2. Consider the so-called Pauli operators ôx = [0)(1| + |1)(0], ôy = −i|0)(1| +i|1)(0| and ôz = 0) (0||11], where {[0), [1}} form an orthonormal basis of the considered Hilbert space. (c) Solve the eigenvalues and the corresponding eigenstates of each Pauli operator using the matrix form, and write the eigenstates using the ket vectors [0) and |1). (d) For each Pauli operator, show that the eigenstates are orthogonal.

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2. Consider the so-called Pauli operators ôx = 0) (1| + |1)(0], ôy = −i|0)(1| +i|1)(0] and ôz = 0) (0 - 1)(1], where {10), 11)} form an orthonormal basis of the considered Hilbert space. (c) Solve the eigenvalues and the corresponding eigenstates of each Pauli operator using the matrix form, and write the eigenstates using the ket vectors [0) and 1). (d) For each Pauli operator, show that the eigenstates are orthogonal.
Transcribed Image Text:2. Consider the so-called Pauli operators ôx = 0) (1| + |1)(0], ôy = −i|0)(1| +i|1)(0] and ôz = 0) (0 - 1)(1], where {10), 11)} form an orthonormal basis of the considered Hilbert space. (c) Solve the eigenvalues and the corresponding eigenstates of each Pauli operator using the matrix form, and write the eigenstates using the ket vectors [0) and 1). (d) For each Pauli operator, show that the eigenstates are orthogonal.
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