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In the book i'm reading i've come to a question regarding degenerate states in one dimension. It says that in one dimension there are no degenerate bound states.

But say I have a stationary state with some energy E, and assume that it is normalizable. You can easily show that the complex conjugate of this state also solves the time-independent Schrodinger eq with the same energy E. The conjugate state must also be normalizable, and as far as I can tell the two are linearly independent?

Does that not disprove the statement? Where am I going wrong in my thinking here?

Thanks,

Jon.

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# In one dimension there are no degenerate bound states?

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