where the q i
are appropriate coordinates for the particular system. Since the form of the coordinates is
not specifi ed, the q i
are referred to as generalized coordinates. Because ψ describes the system in some
particular state, the state is known as the quantum state and ψ is called the state function or complete wave
function .
There needs to be some physical interpretation of the wave function and its relationship to the state of
the system. One interpretation is that the square of the wave function, ψ
2 , is proportional to the prob-
ability of fi nding the parts of the system in a specifi ed region of space. For some problems in quantum
mechanics, differential equations arise that can have solutions that are complex (contain ( 1)
1/2 i ).
In such a case, we use ψ * ψ , where ψ * is the complex conjugate of ψ . The complex conjugate of a func-
tion is the function that results when i is replaced by i . Suppose we square the function ( a ib ):
()22 a ib a aib i b a aib b 22 22 2 2
(2.4)
where the q i
are appropriate coordinates for the particular system. Since the form of the coordinates is
not specifi ed, the q i
are referred to as generalized coordinates. Because ψ describes the system in some
particular state, the state is known as the quantum state and ψ is called the state function or complete wave
function .
There needs to be some physical interpretation of the wave function and its relationship to the state of
the system. One interpretation is that the square of the wave function, ψ
2 , is proportional to the prob-
ability of fi nding the parts of the system in a specifi ed region of space. For some problems in quantum
mechanics, differential equations arise that can have solutions that are complex (contain ( 1)
1/2 i ).
In such a case, we use ψ * ψ , where ψ * is the complex conjugate of ψ . The complex conjugate of a func-
tion is the function that results when i is replaced by i . Suppose we square the function ( a ib ):
()22 a ib a aib i b a aib b 22 22 2 2
(2.4)
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