We　propose　a　simulation　strategy　which　uses　a　classical　device　of　linearly　coupled　chain　of　springs　to　simulate　quantum　dynamics,　in　particular　quantum　walks.　Through　this　strategy,　we　obtain　the　quantum　wave　function　from　the　classical　evolution.　Specially,　this　goal　is　achieved　with　the　classical　momenta　of　the　particles　on　the　chain　and　their　Hilbert　transform,　from　which　we　construct　the　many-body　momentum　and　Hilbert　transformed　momentum　pair　correlation　functions　yielding　the　real　and　imaginary　parts　of　the　wave　function,　respectively.　With　such　a　wave　function,　we　show　that　the　classical　chain＇s　energy　and　heat　spreading　densities　can　be　related　to　the　wave　function＇s　modulus　square.　This　relation　provides　a　new　perspective　to　understand　ballistic　heat　transport.　The　results　here　may　give　a　definite　answer　to　Feynman＇s　idea　of　using　a　classical　device　to　simulate　quantum　physics.　©　2017　American　Physical　Society.