Pauli Matrices Calculator

Analyze spin-1/2 states and operators

Enter real components (will be normalized automatically)

Alpha (spin-up coefficient):

Beta (spin-down coefficient):

Measurement Direction theta (degrees from z-axis):

Measurement Direction phi (degrees in xy-plane):

Normalized Spinor

|psi> = (1.0000, 0.0000)^T

Bloch Sphere Coordinates

theta = 0.00 degrees

Z-Measurement Probabilities

P(spin up) = 100.00%

P(spin down) = 0.00%

Expectation Values (in units of hbar/2)

<sigma_x> = 0.0000

<sigma_y> = 0.0000

<sigma_z> = 1.0000

Pauli Matrix Actions

sigma_x|psi> = (0.0000, 1.0000)^T

sigma_y|psi> = (0.0000i, 1.0000i)^T

sigma_z|psi> = (1.0000, 0.0000)^T

sigma_x = [[0,1],[1,0]]

sigma_y = [[0,-i],[i,0]]

sigma_z = [[1,0],[0,-1]]

S_i = (hbar/2) * sigma_i