Quantum Mechanics in Simple Matrix Form
This elementary text introduces basic quantum mechanics to undergraduates with no background in mathematics beyond algebra. Containing more than 100 problems, it provides an easy way to learn part of the quantum language and apply it to problems.
Emphasizing the matrices representing physical quantities, it describes states simply by mean values of physical quantities or by probabilities for possible values. This approach requires using the algebra of matrices and complex numbers together with probabilities and mean values, a technique introduced at the outset and used repeatedly. Students discover the essential simplicity of quantum mechanics by focusing on basics and working only with key elements of the mathematical structure--an original point of view that offers a refreshing alternative for students new to quantum mechanics.
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algebra axis Bell inequalities Bohr model calculate changes of coordinates characterize rotations commutation relations commutes with J1 complex number consider continuous range deﬁnite value described direction combination E. P. Wigner Einstein electron and nucleus equation example ﬁnd ﬁrst ﬁxed formulas Galilei transformations Heisenberg identity rotation imaginary numbers inverse isJ3 magnetic moment matrices J1 matrices that represent Matrix Mechanics mean value momentum matrices multiplying non-negative real quantity orbital angular momentum oscillator energy pairs of values particle Pauli matrices position and momentum position coordinates possible values q-numbers Q3 and P1 quantized quantum mechanics radiation real numbers reference directions represent physical quantities represent real quantities represented by 21 represented by matrices represents a non-negative represents the product rotation by 180 satisﬁed satisfy the commutation Show small rotations space translations spin and magnetic spin angular momentum spin is zero square Suppose total spin translations and rotations vector quantity velocity