Is the Laplacian operator (LZ) Hermitian in quantum mechanics? What are the implications of Hermiticity in the context of quantum mechanics? Does LZ satisfy the conditions for Hermiticity? How does the Hermiticity of LZ relate to the conservation of probability in quantum systems? Are there any real-world applications where the Hermiticity of LZ plays a crucial role? Explain the mathematical basis behind the Hermiticity of LZ and provide a step-by-step derivation to support your explanation.
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